# Important Questions Class 9 Maths Chapter 3

### Important Questions Class 9 Mathematics Chapter 3 – Coordinate Geometry

In Class 9 Mathematics, students will learn how to locate the points in a cartesian system or an XY plane throughout the chapter on coordinate geometry. This concept is useful for locating an object in a specific location. Locating points on a map or globe is its main application. In this chapter, you will also learn about terms related to the coordinate plane, as well as terms related to the Cartesian plane.

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Our question and answer solution of Important Questions Class 9 Mathematics Chapter 3 will aid in your preparation for the upcoming board exams as well as assist you in getting excellent scores on the exams. We have focused on preparing you for the Class 9 exam using the CBSE curriculum. Your mathematical knowledge will be enhanced by regularly practising questions from our question bank of Important Questions for Class 9 Mathematics Chapter 3, which will also help you grasp the topic better.

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### Important Questions Class 9 Mathematics Chapter 3 – With Solutions

We advise students to solve questions from our question bank of Important Questions for Class 9 Mathematics Chapter 3 to gain a deeper understanding of the topics covered in Coordinate Geometry.

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Given below is a list of questionnaires and their answers from our question set of Important Questions for Class 9 Mathematics, Chapter 3.

Question 1: Point (–3, 5) lies in the

Explanation:

(-3,5) is in the form of (-x,y).

In the given point (-3, 5), the abscissa is negative, and the ordinate is positive. So, it lies in the second quadrant.

Question 2: Signs of abscissa and ordinate of any given point in the second quadrant are respectively

1. +, –
2. –, –
3. –, +
4. +, +

Solution 2: (C) –, +

Explanation:

The signs of the abscissa and ordinate of a given point in the second quadrant are negative and positive respectively.

Question 3:  Point (0, –7) lies

1. on the x-axis
3. on the y-axis

Solution 3: (C) on the y-axis

Explanation: Since the abscissa of the Point is 0, Point (0, –7) lies on the y-axis.

Question 4: Point (– 10, 0) will lie

1. in the negative direction of the x-axis
2. in the negative direction of the y-axis

Solution 4: (A) on the negative direction of the x-axis

Explanation: Point (– 10, 0) predominantly lies in the negative direction of the x-axis.

Question 5:  Abscissa of all the given points on the x-axis is

1. 1
2. 0
3. 2
4. any number

Solution 5: (D)  any number

Explanation: The abscissa of the points on the x-axis can be any number.

Question 6: Ordinate of all the given points on the x-axis is

1. 0
2. – 1
3. 1
4. any number

Solution 6: (A)  0

Explanation: The ordinate of all the given points on the x-axis is 0.

Question 7: The Point at which the two coordinate axes converge is called the

2. ordinate
3. origin
4. abscissa

Solution 7:

(C)  origin

Explanation: The points where the two coordinate axes exactly meet are called the origin.

Question 8: A point both of whose coordinates are negative will be lying in

Explanation: A point whose both coordinates are negative will lie in the III quadrant.

Question 9: Points such as (1, – 1), (2, – 2), (4, – 5), (– 3, – 4)

1. will lie in IV quadrant
2. wil lie in III quadrant
3. will lie in II quadrant
4. will not lie in the same quadrant

Solution 9: (D)  will not lie in the same quadrant

Explanation:

Points like (1, – 1), (2, – 2), (4, – 5) lie in the IV quadrant and (– 3, – 4) lie in III quadrants.

Question 10: If the y coordinate of a point taken as zero, then this Point always lies

2. on y-axis
3. on x-axis

Solution 10:

1. on x-axis

Explanation: We know that if the y-coordinate of a point is zero (ordinate), then this Point always lies on

x-axis.

Question 11:  The given points (–5, 2) and (2, – 5) will lie in the

2. IV and II quadrants, respectively
3. II and IV quadrants, respectively
4. II and III quadrants, respectively

Solution 11: (C) on x-axis

Explanation:

(-5,2) is in the form (-x,y), so it lies in the II quadrant.

(2,-5) is in the form (x,-y), so it lies in the IV quadrant.

(C) II and IV quadrants, respectively

Question 12: If the perpendicular distance of the given point P from the x-axis is 5 units and the foot of the perpendicular lies in the negative direction of the x-axis, then the point P has

1. y – coordinate = – 5 only
2. y – coordinate = 5 only
3. x – coordinate = – 5
4. y – coordinate = 5 or –5

Solution 12: (D) y – coordinate = 5 or –5

Explanation:

Perpendicular distance from the x-axis = 5= Ordinate

The negative direction of the x-axis doesn’t decide the sign of the ordinate.

Question 13:

The points when the abscissa and ordinate have different signs will lie in

Solution 13:(d)

Explanation: The points will be of the form (-x, y) or (x, – y)if the abscissa and ordinate have different signs and these points will lie in II and IV quadrants.

Question 14:

The Point whose ordinate is 4 and lies on K-axis is

(a)(1,4)         (b) (0,4)            (c)    (4,0)           (d) (4,2)

Solution 14: (b)

Explanation: Given the ordinate of any point is 4, and the Point lies on Y-axis, thus its abscissa is zero. Hence, the estimated Point is (0, 4).

Question 15:

Which of the following points P(0, 3), Q(l, 0), R(0, – 1), S(-5, 0) and T(1, 2) does not lie on the X-axis?

(a)    Q, S and T           (b)Q and S only        (c)P, R and T             (d)P and R only

Solution 15: (c)

Explanation: We are aware that a point will lie on the X-axis if it has the coordinates (x, 0), which means that its y-coordinate is zero. Points P (0, 3), R (0, -1), and T (1, 2) in this case does not lie on the X-axis since their y-coordinates are not zero.

Question 16:

The Point lying on the Y-axis at a distance of 5 units and in the negative direction of Y-axis is

(a) (0,5)         (b) (-5,0)     (c) (0,-5)            (d) (5,0)

Solution 16: (C)

Explanation: The fact that the Point is on the X-axis indicates that its ^-coordinate is zero. Additionally, its y-coordinate is negative because it is 5 units away from the X-axis in the opposite direction.

Thus, the required Point is (0, – 5).

Question 17:

The perpendicular distance of the point P(3, 4) from the Y-axis is

(a) 3           (b)    5     (c) 4             (d) 7

Solution 17: (a)

Explanation: We are aware that a point’s abscissa, or x-coordinate, is the angle of that Point with respect to the Y-axis. As a result, point P(3, 4)’s distance from the Y-axis  is equal to 3.

Question 18: The distance of the given Point (-3, -2) from the x-axis is

(a) 2 units

(b) 3 units

(c) 5 units

(d) 13 units

Solution 18:  (a) 2 units

The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis.

Question 19: The distance of the given Point (-6, -2) from the y-axis is

(a) 6 units

(b) 8 units

(c) 2 units

(d)  10 units

Solution 19:  (a) 6 units

The magnitude or absolute value of the Point’s x coordinate is its distance from the y axis.

Question 20: The abscissa and ordinate of the given Point with Coordinates (8, 12) is

(a) abscissa 12, ordinate 8

(b) abscissa 8, ordinate 12

(c) abscissa 0 and ordinate 20

(d) none of these

Solution 20:  (a) abscissa 12 and ordinate 8

The abscissa is the y coordinate of the Point and the ordinate is the x coordinate value.

Question 21: The coordinate of origin in

(a) (X, 0)

(b) (0, y)

(c) (0, 0)

(d) none of these.

Solution 21: (c) (0, 0)

Explanation: For the origin, both abscissa and ordinate are 0.

Question 22: The distance of the Point (2,3) from y- axis  is

(A) 2 units

(B) 3 units

(C) 5 units

(D) 13 units

Solution 22:  (A) 2 units

Explanation: The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis. The magnitude or absolute value of the Point’s x coordinate is what determines how far the Point is from the y-axis.

Question 23: The point (-2, -1) lies in

Explanation: Negative x and y values relate to the third quadrant.

Question 24: The Point (3,0) lies on

(A) +ve x-axis

(B) – ve x-axis

(C) + ve y-axis

(D) –ve y-axis

Solution 24: (A) +ve x axis

Explanation: Because the x-coordinate is positive and the y-coordinate is  zero.

Question 25: The distance of the Point (3, 5) from the x-axis is

(a) 3 units

(b) 4 units

(c) 5 units

(d) 6 units

Solution 25:  (c) 5 units

Explanation: The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis. The magnitude or absolute value of the Point’s x coordinate is what determines how far the Point is from the y-axis.

Question 26: The Point (0, -5) lies on

(a) +ve x-axis

(b) +ve y-axis

(c) –ve x-axis

(d) –ve y-axis

Solution 26:  (d) –ve y-axis

Explanation: When the y coordinate is negative and the x coordinate is zero.

Question 27: The point (-2, 5) lies in

Explanation: The x-values are negative and the y-values are positive in the second quadrant.

Question 28: The distance of the Point (3, 0) from the x-axis is

(a) 3 units

(b) 0 units

(c) 9 units

(d) none of these

Solution 28:  (a) 3 units.

Explanation: The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis. The magnitude or absolute value of the Point’s x coordinate is what determines how far the Point is from the y-axis.

Question 29: The points (other than the origin) whose abscissa is equal to the ordinate lie in

2. b) Quadrant I and II
3. c) Quadrant I & III

Solution 29: (c) quadrant I & III.

Explanation: In I and  III quadrants, the axes will have the same sign.

Question 30:The perpendicular distance of the given point P(4,3) from the y axis is

1. a) 3 Units
2. b) 4 Units
3. c) 5 Units
4. c) 7 Units

Solution 30:  (a) 3 units

The Point  x coordinate indicates how far it is from the Y- axis.

Question 31:The area of triangle OAB with points 0(0,0), A(4,0) & B(0,6) is

1. a) 24 sq. units
2. b) 12 sq. units
3. c) 8 sq. unit
4. d) 16 sq. units

Solution 31:  (b) 12 sq. units.

Explanation: The triangle’s area is equal to the product of its base and height.

Question 32:  Plot the points A(2, 5), B(–2, 2) and C(4, 2) on graph paper. Join AB, BC and AC. Calculate the area of ∆ABC.

Solution 32:

Abscissa of D = Abscissa of A = 2

Ordinate of D = Ordinate of B = 2

Now,

BC = (2 + 4) units = 6 units

AD = (5 – 2) units = 3 units

Area of ΔABC= 12×Base×Height

=12×6×3

=9

Hence, area of ∆ABC is 9 square units

Question 33: Predict whether the given statements are True / False? Give justification for your answer.

(i) Point (3, 0) lying in the first quadrant.

(ii) Points (1, –1) and (–1, 1) lying in the same quadrant.

(iii) The coordinates of a point whose ordinate is – ½ and abscissa is 1 are – ½ , 1.

(iv) A point lying on the y-axis at  2 units distance from the x-axis. Its coordinates are (2, 0).

(v) (–1, 7) is a point lying in the II quadrant.

Solution 33:

(i) The Point (3, 0) lies in the first quadrant.

False

Explanation:

The ordinate of the given Point (3, 0) is given zero.

Hence, the Point must lie on the x-axis

(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.

False

Explanation:

(1, -1) lies in IV quadrant

while (-1, 1) lies in II quadrant.

(iii) The coordinates of a point for which ordinate is – ½ and abscissa is 1 are – ½ , 1.

False

Explanation:

The coordinates of a point for which ordinate is – ½ and abscissa is 1 is (1, -1/2).

(iv) A point is lying on the y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0).

False

Explanation:

A point is lying on the y-axis at a distance of 2 units from the x-axis. Thus its coordinates are (0, 2).

(v) (–1, 7) is a point lying in the II quadrant.

True

Explanation:

(–1, 7) is a point in the II quadrant.

Question 34:

In which quadrant or axis on the following points will lie?

(-3, 5),  (2,0), (2, 2), (-3,-6),(4,-1),

Solution 34:

(i) For point (-3, 5), the x-coordinate is negative while y-coordinate is positive, so it  is lying in II quadrant.

(ii) For point (4,-1), the x-coordinate is positive while the y-coordinate is negative, so it lies in the IV quadrant.

(iii) In Point (2,0), the x-coordinate is positive while the y-coordinate is zero, so it lies on the X-axis.

(iv) In Point (2,2), both x-coordinate and y-coordinate are positive, so it lies in the I quadrant.

(v) In Point (-3, – 6), x-coordinate and y-coordinate both are negative, so it lies in III quadrant.

Question 35: Write the coordinates of the points P, Q, R, S, T and O from the figure given below.

Solution 35:

The coordinates of points P, Q, R, S, T and O are as follows:

P = (1, 1)

Q = (-3, 0)

R = (-2, -3)

S = (2, 1)

T = (4, -2)

O = (0, 0)

Question 36: Without plotting the points find the quadrant in which they will lie, if

(i) ordinate is 5 while abscissa is – 3

(ii) abscissa is – 5 while ordinate is – 3

(iii) abscissa is – 5 while ordinate is 3

(iv) ordinate is 5 while abscissa is 3

Solution 36:

(i) The Point is (-3,5).

Hence, the Point is lying in the II quadrant.

(ii) The Point is (-5,-3).

Hence, the Point is lying in the III quadrant.

(iii) The Point is (-5,3).

Hence, the Point is lying in the II quadrant.

(iv) The Point is (3,5).

Hence, the Point is lying in the I quadrant.

Question 37:

Three vertices of any rectangle ABCD are A(3, 1), B(–3, 1) and C(–3, 3). Plot these points on the graph paper and find the coordinates of the fourth vertex D. Also, find the area of rectangle ABCD.

Solution 37:

Let A(3, 1), B(–3, 1) and C(–3, 3) be three vertices of a rectangle ABCD.

Let the y-axis cut the rectangle ABCD at the points P and Q respectively.

Abscissa of D = Abscissa of A = 3.

Ordinate of D = Ordinate of C = 3.

∴ coordinates of D are (3, 3).

AB = (BP + PA) = (3 + 3) units = 6 units.

BC = (OQOP) = (3 – 1) units = 2 units.

Ar(rectangle ABCD) = (AB × BC)

= (6 × 2) sq. units

= 12 sq. units

Hence, the area of rectangle ABCD is 12 square units.

Question 38:

Which of the following points is lying on the Y-axis?

A(l, 1), B(1, 0), C(0, 1), D(0, 0), E(0, -1), F(-1, 0), G(0, 5), H(-7, 0) and I(3 ,3).

Thinking Process

The Point lying on the Y-axis means the x-coordinate of the Point will be zero. Check this condition for each and every given Point and find out the correct Point.

Solution 38:

We know that a point will be lying on the Y-axis, if its x-coordinate is zero. Given, x-coordinate of the points C(0, 1), D(0, 0), E(0,-1) and G(0, 5) are zero. So, these points tend to lie on the Y-axis. Also, D(0, 0) is the Point of intersection for both the axes, so we can consider that it lies on the Y-axis as well as on the X-axis.

Question 39: In the figure given below, LM is a parallel line to the y-axis at 3 units distance.

(i) What will be the coordinates of points P, R and Q?

(ii) What is the difference between the abscissas of points L and M?

Solution 39:

(i) The given coordinates are:

P = (3,2)

R = (3,0)

Q = (3,-1)

(ii) Since, all the points lying on the line have the same abscissa = 3.

The difference in abscissas of L and M is 0.

Question 40:

Find the possible coordinates of the Point

(i) which lies both on X and Y-axes .

(ii) whose ordinate is – 4 and lies on the Y-axis.

(iii) whose abscissa is 5 and lies on the X-axis.

Solution 40:

(i) The Point which lies both on the X and Y-axes  is the origin and the coordinates are (0, 0).

(ii) The Point having ordinate – 4 and lies on Y-axis, i.e., the x-coordinate is zero, is (0,-4).

(iii) The Point whose abscissa is 5 and lies on X-axis, and the y-coordinate is zero, is (5, 0).

Question 41: See the figure given below and complete the following statements:

(i) The abscissa and the ordinate of any point B are _ _ _ and _ _ _, respectively.

Hence, the coordinates of B are (_ _, _ _).

(ii) The x-coordinate and the y-coordinate of any point M are _ _ _ and _ _ _,

respectively. Hence, the coordinates of M are (_ _, _ _).

(iii) The x-coordinate and the y-coordinate of any point L are _ _ _ and _ _ _,

respectively. Hence, the coordinates of L are (_ _, _ _).

(iv) The x-coordinate and the y-coordinate of any point S are _ _ _ and _ _ _,

respectively. Hence, the coordinates of S are (_ _, _ _).

Solution 41: (i) Since the distance of point B from the y – axis is 4 units, the x – coordinate or abscissa of point B is 4. The distance of point B from the x-axis is 3 units; therefore, the y – coordinate, i.e., the ordinate of point B is 3.

Thus, the coordinates of point B are (4, 3).

As in (i) above :

(ii) The x – coordinate and the y – coordinate of Point M are –3 and 4, respectively.

Hence, the coordinates of point M are (–3, 4).

(iii) The x – coordinate and the y – coordinate of point L are –5 and – 4, respectively.

Thus, the coordinates of any point L are (–5, – 4).

(iv) The x – coordinate and the y- coordinate of point S are 3 and – 4, respectively.

Thus, the coordinates of point S are (3, – 4).

Question 42:  How will you describe the table lamp position on your study table to another person?

Solution 42:

We use two lines, a perpendicular and a horizontal line, to describe the location of the table lamp on the study table. Using the horizontal and perpendicular lines as the X and Y axes of the table, respectively, and the perpendicular line as the Y axis. Consider the intersection of the X and Y axes in one of the table’s corners as the origin. The table’s length is now its Y axis, and its width is its X axis. Create a point by connecting the line from the origin to the table light. It is necessary to compute the Point’s separation from the X and Y axes before expressing the results in terms of coordinates.

The table lamp will be in the coordinates (x, y) because the Point is separated from the X- and Y-axis by x and y, respectively.

Here, (x, y) = (15, 25)

Question 43: Write the answer for the following questions:

(i) What is the name of the lines that are drawn horizontally and vertically to represent the positions of all points in the Cartesian plane?

(ii) What are the names of the various components of the plane that these two lines form?

(iii) Indicate the name of the intersection location of these two lines.

Solution 43:

(i) The x-axis and y-axis are the names of the horizontal and vertical lines drawn to calculate the position of any point in the Cartesian plane.

(ii) The quadrants are the names of each section of the plane created by the x-axis and y-axis.

(iii)The origin is the location where these two lines intersect.

Question 44: Without plotting any of the points, indicate the quadrant in which they will lie, if

(i) the ordinate is 5 while abscissa is – 3

(ii) the abscissa is – 5 while the ordinate is – 3

(iii) the abscissa is – 5 while ordinate is 3

(iv) the ordinate is 5 while abscissa is 3

Solution 44:

(i) The Point is (-3,5).

Therefore, the Point lies in the II quadrant.

(ii) The Point is (-5,-3).

Therefore, the Point lies in the III quadrant.

(iii) The Point is (-5,3).

Therefore, the Point lies in the II quadrant.

(iv) The Point is (3,5).

Therefore, the Point lies in the I quadrant.

Question 45: Write the coordinates of any points marked on the axes in the figure given below.

Solution 45: Part 1

You can see that :

(i) The Point A is at + 4 units distance from the y – axis and at zero distance from the x-axis. Thus, the x – coordinate of A is 4, and the y – coordinate will be 0. Hence, the coordinates of Point A are (4, 0).

(ii) The coordinates of point B are (0, 3).

(iii) The coordinates of point C are (– 5, 0).

(iv) The coordinates of point D are (0, – 4).

(v) The coordinates of E are (23,0).

The y coordinate of any point situated on the x-axis is always zero because every Point on the x-axis is at zero distance from the x-axis. Any point on the x-axis, therefore, has coordinates of the form (x, 0), where x represents the distance of the Point from the y-axis. Similar to the x-axis, any point’s coordinates on the y-axis are of the form (0, y), where y is the Point’s distance from the x-axis.

Part 2: What are the coordinates of the origin O?

Its abscissa and ordinate are both zero since it is at zero distance from both axes. Consequently, the origin’s coordinates are (0, 0).

It is possible that you have noticed the correlation between a point’s coordinate sign and the quadrant in which it  is located.

(i) Since the first quadrant is bounded by the positive x-axis and the positive y-axis, a point in the first quadrant will have the form (+, +).

(ii) Because the second quadrant is bounded by the negative x-axis and the positive y-axis, a point in the second quadrant will have the form (-, +).

(iii)Because the third quadrant is bounded by the negative x-axis and the negative y-axis, a point in the third quadrant will have the form (-, -).

(iv) Given that the fourth quadrant is bounded by the positive x-axis and the negative y-axis, a point in the fourth quadrant will have the form (+, -).

Question 45: Write the answer to the following questions:

(i) What are the names of the lines that are drawn horizontally and vertically to represent the positions of every Point in the Cartesian plane?

(ii) What are the names of the various components of the plane that these two lines form?

(iii) Indicate the name of the intersection location of these two lines.

Solution 45:

(i)  The x-axis and y-axis are the names of the horizontal and vertical lines drawn to calculate the position of any point in the Cartesian plane.

(ii)  Each section of the plane created by the x- axis and y-axis is referred to as a quadrant.

(iii) The Point where these two lines converge is called the origin.

Question 46: On which axis will the given points lie?

1. (7, 0)
2. (0, -3)

iii. (0, 6)

1. (-5, 0)

Solution 46:

1. (7,0) lies on X-axis since the y component is zero
2. (0, -3) lies on Y-axis since the x component is zero

iii. (0,6) lies on Y-axis since the x component is zero

1. (-5,0) lies on X-axis since the y component is zero

Question 47: In which quadrants will the given points lie?

1. (4, -2)
2. (-3, 7)

iii. (-1, -2)

1. (3, 6)

Solution 47:

1. The x component is positive, and the y component is negative. Hence the IV quadrant is (4,-2)
2. Due to the negative x component and the positive y component, the second quadrant is (-3,7).

iii. Due to the negative x and y components, the third quadrant is located at (-1,-2).

1. Since both the x and y components are positive, the Point (3, 6) lies in quadrant I.

Question 48: Does P (3, 2) represent the same Point as Q(2, 3), or not?

Solution 48:  The points P(3,2) and Q(2,3) are not the same, hence the answer is no. Unlike Q, which has an x component of 2 and a y component of 3, the first one has an x component of 3 and a y component of 2.

Question 49: Locate the given points (5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and

(6, 1) in the Cartesian plane.

Solution 49 : We take 1cm = 1 unit; we now draw the x-axis and the y – axis. The positions of

the given points are shown by dots in figure below

You can see that the positions of (0, 5) and (5, 0) are not identical. The placements of (2, 5) and (5, 2) are also different. Additionally, the positions of (-3, 5) and (-5, -3) are different. You can demonstrate this by using multiple instances to show that if x y, then the positions of (x, y) in the Cartesian plane are not the same (y, x). The position of (y, x) will be different from the position of (y, x) if the coordinates x and y are switched (x, y). This implies that it’s crucial to consider x and y’s order when (x, y).

Therefore, (x, y) is called an ordered pair. The ordered pair (x, y) ≠ ordered pair (y, x) if x ≠ y. Also (x, y) = (y, x), if x = y.

Question 52: Find the coordinates of Point equidistant from the given two points P(3,0) and Q(-3,0). How many points possibly satisfy this condition?

Solution 52:  All the points on the Y-axis satisfy this condition.

Question 53: Plot the following given ordered pairs (x, y) of numbers as points in the Cartesian plane. Using the scale 1cm = 1 unit on the axes.

Solution 53 : The pairs of numbers represented in the table can be indicated by the points

(– 3, 7), (0, –3.5), (– 1, – 3), (4, 4) and (2, – 3). The locations of the given points are shown

by dots in the figure given below.

Question 54: Name each part of the given plane formed by the Vertical and horizontal lines.

Solution 54:  The vertical line is called the y-axis and the horizontal line is called the x-axis. And these form four quadrants.

Question 55: Write the mirror image of the given Point (2, 3) and (-4, -6) with respect to the x-axis.

Solution 55:  The mirror image of the given Point (2, 3) is (2, -3) with respect to the x-axis.

The mirror image of the Point (-4, -6) is (-4,6) with respect to the x-axis.

Question 56: Write the abscissa and ordinate of a point (-3, -4)

Solution 56:  The Abscissa will be -3 and ordinate will be -4

Question 57: State the quadrant in which each of the following points will lie:

(i) (2, 1)

(ii) (-7,11)

(iii) (-6, -4)

(iv) (-5, -5)

Solution 57:  (2, 1) lie in the I quadrant

(-7, 11) lie in the II Quadrant

(-6, -4) lie in the III Quadrant

(-5, -5) lie in the III Quadrant

Question 58: What is the name of the horizontal and vertical lines which are  drawn to determine the position of any given point in the Cartesian plane?

Solution 58:  The horizontal line is called the x-axis while the vertical line is called the y – axis

Question 59: List the points on the plane that do not fall into any of the four quadrants.

Solution 59: The points in a plane that do not belong to any one of the quadrants is origin and are denoted by point O (0,0).

Question 60: Which of the given points belong to the x-axis?

(a) (2, 0) (b) (3, 3) (c) (0, 1) (d) (-2, 0)

Solution 60: (2, 0) and (-2, 0) belong to the x- axis.

For the Point to belong to the y-axis, the y-component must be zero.

Question 61: Which of the given points belongs to the 1st quadrant

(a) (3, 0) (b) (1, 2) (c) (-3, 4) (d) (3, 4)

Solution 61: (1, 2) and (3, 4) belong to the 1st quadrant.

Question 62: Which of the given points belongs to 3rd quadrant

(a) (1, 3) (b) (-1, -3) (c) (0, 4) (d) (-4, -2)

Solution 62: (-1, -3) and (-4, -2) belong to the 3rd quadrant.

Question 63: Answer each of the following questions:

(i) In order to locate any point in the Cartesian plane, what is the name of the horizontal and vertical lines that are drawn?

Solution (i):  The x-axis and the y-axis are the lines that are drawn to determine the positions of any points in the Cartesian plane, respectively.

(ii)  What are the names of the various components of the plane that these two lines form?

Solution (ii):  The term “quadrant” refers to each section of the plane that is created by the x- and y-axes.

(iii)  Indicate the name of the intersection location of these two lines.

Solution (iii): The origin, symbolised by O, is the location where the x- and y-axes connect (0,0).

Question 64: Find the ordered pairs of the linear equation

2x+y=4

2x+y=4

and plot them as ‘how many such ordered pairs can be present and plotted?

Solution 64: The given equation is

2x+y=4

2x+y=4

The equation will hold if

x=0,y=4

x=0,y=4

thus, (0, 4),

x=1,y=2

x=1,y=2

thus, (1, 2),

x=2,y=0

x=2,y=0

thus,(2, 0) ,

x=3,y=−2

x=3,y=−2

i.e. (3, -2)…

Likewise, (4,-4), (5,-6), (-1,6), (-2,8) etc. also. These are a few ordered pairs which are

valid solutions. And  such ordered pairs are infinite.

Question 65: What is coordinate geometry?

Solution 65: In order to present geometric forms in a two-dimensional plane and learn about their properties, coordinate geometry is a crucial area of mathematics. In order to get a basic concept of coordinate geometry, we’ll try to learn about the coordinate plane and a point’s coordinates here.

Question 66: What is a Coordinate plane?

Solution 66: In order to make it simple to locate the points, a cartesian plane divides the plane space into two dimensions. The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axis of the coordinate plane. The origin is the place where these coordinate axis connect, and they divide the plane into four quadrants (0, 0). Additionally, any point in the coordinate plane is denoted by the coordinates (x, y), where x represents the Point’s position in relation to the x-axis and y represents its position in relation to the y-axis.

Question 67: What are the properties of a point?

Solution 67: The properties of the Point in the coordinate plane’s four quadrants are as follows:

• The origin O is the location where the x- and y-axes intersect, and its coordinates are (0, 0).
• The positive x-axis is to the right of the origin O, while the negative x-axis is to the left of the origin O. Additionally, the positive and negative y-axis are located above and below the origin O, respectively.
• The first quadrant’s Point (x, y) is plotted with reference to the positive x-axis and the positive y-axis because it has both positive values.
• With reference to the negative x-axis and positive y-axis, the point (-x, y) in the second quadrant is drawn.
• Plotting is done with reference to the negative x-axis and negative y-axis for the Point depicted in the third quadrant (-x, -y).
• The positive x-axis and the negative y-axis are used to plot the Point (x, -y) that is located in the fourth quadrant.

Question 68: Explain the coordinates of a point.

Solution 68:

Image source: Internet

An address that aids in locating a spot in space is a coordinate. The coordinates of a point in a two-dimensional space are (x, y). Let’s note these two crucial terms right now.

• Abscissa:  The distance from the origin along the x-axis is represented by the x value at the Point (x, y).
• Ordinate:  It is the y value at the coordinates (x, y) and the angle at which the Point lies in relation to the x-axis, which runs parallel to the y-axis.

A point’s coordinates can be used for a variety of tasks, including calculating distance, midpoint, a line’s slope, and its equation.

Question 69: Write the distance formula in coordinate geometry.

Solution 69: The square root of the sum of squares of the difference between the x coordinate and the y coordinate of the two supplied points is equal to the distance between two points (x1, y1) and (x2, y2) in this example. The following is a formula for calculating the separation between two points.

D = (x2 – x1)2 + (y2 – y1)2

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Q.1 Plot the following points in a Cartesian plane:

(-2,4), (3,-1), (-1, 0), (1, 2) & (-3, -5)

Marks:4 Ans

Q.2 Which of the following points:

B(1, 0), C(0,1 ), E (-1, 0),  F ( 0, -1),  G (4, 0),  H (0, -7)

(i) lie on x ?axis?

(ii) lie on y ? axis?

Marks:3 Ans

(i)The point whose ordinate is 0 lies on x axis.

Therefore, the point B (1,0), E (-1,0), G(4,0) lie on x axis.

(ii) The point whose abscissa is 0 lies on y  axis.

Therefore, the points C (0,1), F (0,-1) , H (0,-7) lie on y-axis.

Q.3 See the figure, and write the following:

1)  The coordinates of B.

2)  The point identified by the point (-3, -5).

3) The abscissa of point D.

4) The ordinate of the point E.

5)  The point identified by the coordinates (2, -4).

Marks:4 Ans

1) Coordinate of B(2, 2).

2) A(-3, -5)

3) Abscissa of point D is 5.

4) Ordinate of point E is -4.

5) E(2, -4)

Q.4 The coordinates of the vertices of the triangle ABC, as shown in the figure, are __________________.

1. (2, 2), (1,3) and (1, 0) / (2, 2), (1, 3) and (1, 0)
2. (2, 2), (1, 3) and (0, 1) / (2, 2), (1, 3) and (0, 1)
3. (2, 2), (1, 3) and (1, 0) / (2, 2), (1, 3) and (1, 0)
4. (2, 2), (?1, 3) and (0, 1) / (2, 2), (1, 3) and (0, 1)

Marks:1 Ans

(2, 2), (1, 3) and (1, 0)

Q.5 After walking 6 units in the direction parallel to the x-axis to the left of the origin, Jacob reaches point P. If he started from the point (1, 2), then the coordinates of point P are _____________.

1. ( 5, 2) (5, 0)
2. (4, 2) (4, 2)
3. ( 5, 2) (5, 0)
4. (4, 2) (4, 2)

Marks:1 Ans

( 5, 2)