The Use of Coordinates is a coordinate geometry chapter that uses two perpendicular number lines to locate points on a plane. Important Questions Class 9 Maths Chapter 1 cover the Cartesian plane, x-axis, y-axis, origin, quadrants, coordinates, distance between two points, midpoint reasoning, and real-life coordinate applications.
Coordinates help us describe exact locations. A room plan, city grid, mobile screen, map, and chessboard all use the same idea: a position can be written using two numbers.
Class 9 Maths Chapter 1 builds this idea from the basics. Students first learn axes, origin, quadrants, and ordered pairs. Then they use the Baudhāyana-Pythagoras theorem to find the distance between two points. This makes the chapter important for geometry, graphs, and later coordinate-based questions.
Key Takeaways
| Topic |
What to Revise |
| Cartesian Plane |
x-axis, y-axis, origin, coordinate plane |
| Origin |
Point where both axes meet: (0, 0) |
| Quadrants |
Sign patterns in four regions |
| Ordered Pair |
Coordinates written as (x, y) |
| Points on Axes |
(x, 0) on x-axis and (0, y) on y-axis |
| Distance Formula |
Used to find distance between two points |
| Midpoint |
Average of endpoint coordinates |
| Collinearity |
Checked using distances or coordinate reasoning |
| Applications |
Room plans, city grids, screen coordinates |
| Common Mistakes |
Sign errors, reversed coordinates, wrong axis |
Class 9 Maths Chapter List
Important Topics in Class 9 Maths Chapter 1 The Use of Coordinates
Class 9 maths chapter 1 important questions are mostly based on signs, axes, coordinate reading, distance formula, and real-life plotting.
Students should revise the basic coordinate rules before solving numerical questions. Most mistakes happen because of wrong signs or reversed coordinates.
- Cartesian coordinate system
- x-axis and y-axis
- Origin and coordinates of origin
- Ordered pair (x, y)
- Four quadrants
- Sign convention in each quadrant
- Points on x-axis and y-axis
- Plotting points on the Cartesian plane
- Distance between two points
- Baudhāyana-Pythagoras theorem connection
- Midpoint reasoning
- Collinearity using distances
- Room layout questions
- City-grid coordinate questions
- Screen-coordinate applications
Important Questions Class 9 Maths Chapter 1 with Answers
Important Questions Class 9 Maths Chapter 1 should be practised topic-wise. Start with coordinates and quadrants, then move to distance formula, midpoint, collinearity, and application questions.
These class 9 maths chapter 1 questions and answers cover one-mark, two-mark, numerical, case-based, and HOTS-style questions.
Very Short Answer Questions from The Use of Coordinates
One-mark questions test definitions, axis rules, sign conventions, and coordinate reading.
Use exact terms and avoid long explanations.
Class 9 Maths Chapter 1 Important Questions
Q1. What are the coordinates of the origin?
Ans. The coordinates of the origin are (0, 0).
The origin is the point where the x-axis and y-axis intersect.
Q2. What is the x-coordinate of any point on the y-axis?
Ans. The x-coordinate of any point on the y-axis is 0.
Such points have coordinates of the form (0, y).
Q3. What is the y-coordinate of any point on the x-axis?
Ans. The y-coordinate of any point on the x-axis is 0.
Such points have coordinates of the form (x, 0).
Q4. In which quadrant does the point (-5, 3) lie?
Ans. The point (-5, 3) lies in Quadrant II.
In Quadrant II, x is negative and y is positive.
Q5. In which quadrant does the point (3, -5) lie?
Ans. The point (3, -5) lies in Quadrant IV.
In Quadrant IV, x is positive and y is negative.
Q6. Write the sign convention for Quadrant III.
Ans. In Quadrant III, both coordinates are negative.
The sign convention is (-, -).
Q7. Point B is on the x-axis and 4.5 units to the right of the origin. What are its coordinates?
Ans. The coordinates of B are (4.5, 0).
A point to the right of the origin has a positive x-coordinate. Since it lies on the x-axis, its y-coordinate is 0.
Q8. If x = y, is (x, y) the same as (y, x)?
Ans. Yes.
If x = y, then both ordered pairs are the same.
If x ≠ y, then (x, y) and (y, x) are different points.
Cartesian Plane Class 9 Questions and Answers
The Cartesian plane is formed by two perpendicular number lines.
The horizontal line is the x-axis. The vertical line is the y-axis. Their intersection is the origin.
Short Answer Questions on Cartesian Plane and Quadrants
Q1. State the quadrant in which each point lies: (a) (-3, -7), (b) (4, -2), (c) (-1, 5), (d) (6, 9).
Ans.
| Point |
Sign Pattern |
Quadrant |
| (-3, -7) |
(-, -) |
Quadrant III |
| (4, -2) |
(+, -) |
Quadrant IV |
| (-1, 5) |
(-, +) |
Quadrant II |
| (6, 9) |
(+, +) |
Quadrant I |
Q2. Point W has x-coordinate -5. Point H lies on the line through W parallel to the y-axis. Which quadrants can H lie in?
Ans. A line parallel to the y-axis has the same x-coordinate throughout.
So, H has coordinates of the form (-5, y).
If y > 0, H lies in Quadrant II.
If y < 0, H lies in Quadrant III.
If y = 0, H lies on the x-axis and not in any quadrant.
Q3. Does Q(y, x) ever coincide with P(x, y)? Justify your answer.
Ans. Yes, Q(y, x) coincides with P(x, y) when x = y.
If x and y are not equal, the ordered pairs are different.
Coordinates are position-specific. Changing the order usually changes the point.
Q4. The axes divide the Cartesian plane into four parts. Name these parts and give the sign of coordinates in each.
Ans. The four parts are called quadrants.
| Quadrant |
Sign of Coordinates |
| Quadrant I |
(+, +) |
| Quadrant II |
(-, +) |
| Quadrant III |
(-, -) |
| Quadrant IV |
(+, -) |
Points on the axes are not inside any quadrant.
Q5. Plot R(3, 0), A(0, -2), M(-5, -2), and P(-5, 2). Which two points are mirror images in one axis?
Ans. M(-5, -2) and P(-5, 2) are mirror images in the x-axis.
They have the same x-coordinate. Their y-coordinates are equal in magnitude but opposite in sign.
Coordinates of Points Class 9 Questions
Reading coordinates correctly is the foundation of this chapter.
Always write the x-coordinate first and the y-coordinate second.
Class 9 Maths Chapter 1 Questions and Answers
Q1. Point G is on the y-axis and 4.5 units below the origin. Write its coordinates.
Ans. G = (0, -4.5).
A point on the y-axis has x-coordinate 0. Since G is below the origin, its y-coordinate is negative.
Q2. The corners of Reiaan’s room are O(0, 0), A(12, 0), B(12, 10), and C(0, 10). In which quadrant do B and C lie?
Ans. B(12, 10) lies in Quadrant I because both coordinates are positive.
C(0, 10) lies on the y-axis. It is not inside any quadrant.
Q3. A wardrobe occupies W₁(3, 0), W₂(7, 0), W₃(7, 2), and W₄(3, 2). What are its length and width?
Ans. Length along the x-direction:
|7 - 3| = 4 units
Width along the y-direction:
|2 - 0| = 2 units
So, the wardrobe is 4 units long and 2 units wide.
Q4. A point P lies on the x-axis. Its x-coordinate is negative. In which direction from the origin does P lie?
Ans. P lies to the left of the origin.
Points on the x-axis with negative x-coordinates are located left of the origin.
Q5. Write the coordinates of a point that lies 6 units above the origin on the y-axis.
Ans. The point is (0, 6).
A point on the y-axis has x-coordinate 0. Since it is above the origin, y is positive.
Distance Between Two Points Class 9 Questions
Distance between two points is the most important numerical topic in this chapter.
The distance formula comes from the Baudhāyana-Pythagoras theorem.
Distance between A(x₁, y₁) and B(x₂, y₂):
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance Formula Questions with Answers
Q1. Find the distance between A(3, 4) and D(7, 1).
Ans.
d = √[(7 - 3)² + (1 - 4)²]
= √[4² + (-3)²]
= √[16 + 9]
= √25
= 5 units
Q2. Find the distance between D(7, 1) and M(9, 6).
Ans.
d = √[(9 - 7)² + (6 - 1)²]
= √[2² + 5²]
= √[4 + 25]
= √29 units
So, distance = √29 units.
Q3. Find the distance between M(9, 6) and A(3, 4).
Ans.
d = √[(3 - 9)² + (4 - 6)²]
= √[(-6)² + (-2)²]
= √[36 + 4]
= √40
= 2√10 units
Q4. Find the distance between P(-2, 3) and Q(4, 11).
Ans.
d = √[(4 - (-2))² + (11 - 3)²]
= √[6² + 8²]
= √[36 + 64]
= √100
= 10 units
Q5. Why do negative coordinate differences not affect the distance formula?
Ans. In the distance formula, coordinate differences are squared.
A negative difference becomes positive after squaring.
Example:
(-3)² = 9
So, distance is always non-negative.
Midpoint and Collinearity Questions Class 9 Maths
Midpoint questions use averages of coordinates.
Collinearity questions check whether three points lie on one straight line.
Class 9 Coordinate Geometry Important Questions
Q1. M(-7, 1) is the midpoint of A(3, -4) and B(x, y). Find B.
Ans.
Using midpoint formula:
x-coordinate:
-7 = (3 + x)/2
3 + x = -14
x = -17
y-coordinate:
1 = (-4 + y)/2
-4 + y = 2
y = 6
So, B = (-17, 6).
Q2. Are M(-3, -4), A(0, 0), and G(6, 8) on the same straight line?
Ans.
Find the distances.
MA = √[(0 - (-3))² + (0 - (-4))²]
= √[3² + 4²]
= √25
= 5
AG = √[(6 - 0)² + (8 - 0)²]
= √[6² + 8²]
= √100
= 10
MG = √[(6 - (-3))² + (8 - (-4))²]
= √[9² + 12²]
= √225
= 15
Since MA + AG = MG,
5 + 10 = 15
The points are collinear. A lies between M and G.
Q3. Points A(1, -8), B(-4, 7), and C(-7, -4) lie on a circle centred at the origin. Find the radius.
Ans.
OA = √[1² + (-8)²]
= √[1 + 64]
= √65
OB = √[(-4)² + 7²]
= √[16 + 49]
= √65
OC = √[(-7)² + (-4)²]
= √[49 + 16]
= √65
All three points are at equal distance from the origin.
So, they lie on a circle centred at the origin.
Radius = √65 units.
Q4. Find the midpoint of A(2, 6) and B(8, 10).
Ans.
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
= [(2 + 8)/2, (6 + 10)/2]
= [10/2, 16/2]
= (5, 8)
Exercise-Based and Application Questions from Class 9 Maths Chapter 1
Application questions connect coordinates with room layouts, city grids, and screen positions.
These questions test whether students can use coordinates outside a normal graph.
The Use of Coordinates Class 9 Important Questions
Q1. Reiaan’s rectangular study table has three feet at (8, 9), (11, 9), and (11, 7). Where is the fourth foot?
Ans. The fourth point must complete the rectangle.
The missing point has x-coordinate 8 and y-coordinate 7.
So, the fourth foot is at (8, 7).
Width = |11 - 8| = 3 units
Length = |9 - 7| = 2 units
Q2. A city has two main roads crossing at the centre. Streets run parallel every 200 m, with 10 streets in each direction. How many intersections can be referred to as (4, 3)?
Ans. The coordinate (4, 3) identifies exactly one intersection.
It means the crossing of the 4th north-south street and the 3rd east-west street.
A coordinate pair gives a unique location when the convention is fixed.
Q3. A circular icon of radius 80 pixels is centred at A(100, 150) on an 800 × 600 pixel screen. Does any part of the circle lie outside the screen?
Ans.
Distance from centre to left edge = 100 pixels
Distance from centre to bottom edge = 150 pixels
Distance from centre to right edge = 800 - 100 = 700 pixels
Distance from centre to top edge = 600 - 150 = 450 pixels
The radius is 80 pixels.
Since 80 is less than all four distances, no part of the circle lies outside the screen.
Q4. Two circular icons have radius 80 at A(100, 150) and radius 100 at B(250, 230). Do they intersect?
Ans.
Find distance AB:
AB = √[(250 - 100)² + (230 - 150)²]
= √[150² + 80²]
= √[22500 + 6400]
= √28900
= 170 pixels
Sum of radii = 80 + 100
= 180 pixels
Since 170 < 180, the two circles intersect.
Case-Based Questions from The Use of Coordinates
Case-based questions usually give a real-life diagram or coordinate setting.
Read the coordinates carefully before calculating.
Case Study: Reiaan’s Room
Reiaan’s room has corners O(0, 0), A(12, 0), B(12, 10), and C(0, 10). The bathroom door has ends B₁(0, 1.5) and B₂(0, 4). The room door spans from D₁ to R₁(11.5, 0).
Q1. What are the coordinates of D₁ if the room door is 1.5 units wide and R₁ = (11.5, 0)?
Ans. The door lies on the x-axis.
R₁ = (11.5, 0)
Door width = 1.5 units
D₁ has x-coordinate:
11.5 - 1.5 = 10
So, D₁ = (10, 0).
Q2. How wide is the bathroom door?
Ans. The bathroom door runs from B₁(0, 1.5) to B₂(0, 4).
Width = |4 - 1.5|
= 2.5 units
Q3. Is the bathroom door narrower or wider than the room door?
Ans. Bathroom door width = 2.5 units.
Room door width = 1.5 units.
So, the bathroom door is wider than the room door.
Q4. If the bathroom door opens from hinge B₁(0, 1.5), will it hit the wardrobe corner W₄(3, 2)?
Ans. Door length = 2.5 units.
Distance from B₁(0, 1.5) to W₄(3, 2):
d = √[(3 - 0)² + (2 - 1.5)²]
= √[9 + 0.25]
= √9.25
≈ 3.04 units
Since 3.04 > 2.5, the door will not hit the wardrobe.
MCQs from Class 9 Maths Chapter 1
MCQs test sign convention, axes, coordinates, and formula selection.
Read each ordered pair carefully before choosing the answer.
Class 9 Maths Chapter 1 Extra Questions
Q1. The point (0, -6) lies on:
(a) x-axis
(b) y-axis
(c) Quadrant III
(d) Quadrant IV
Ans. (b) y-axis
Its x-coordinate is 0, so it lies on the y-axis.
Q2. The sign convention in Quadrant IV is:
(a) (+, +)
(b) (-, +)
(c) (-, -)
(d) (+, -)
Ans. (d) (+, -)
In Quadrant IV, x is positive and y is negative.
Q3. The distance between (0, 0) and (6, 8) is:
(a) 8
(b) 10
(c) 12
(d) 14
Ans. (b) 10
Distance = √[6² + 8²]
= √100
= 10 units
Q4. A point on the x-axis has coordinates:
(a) (0, y)
(b) (x, 0)
(c) (x, y)
(d) (0, 0) only
Ans. (b) (x, 0)
Any point on the x-axis has y-coordinate 0.
Q5. Which point lies in Quadrant II?
(a) (4, 5)
(b) (-4, 5)
(c) (-4, -5)
(d) (4, -5)
Ans. (b) (-4, 5)
Quadrant II has negative x-coordinate and positive y-coordinate.
Important Formulas and Rules from Class 9 Maths Chapter 1
| Concept |
Formula / Rule |
| Origin |
(0, 0) |
| Point on x-axis |
(x, 0) |
| Point on y-axis |
(0, y) |
| Quadrant I |
(+, +) |
| Quadrant II |
(-, +) |
| Quadrant III |
(-, -) |
| Quadrant IV |
(+, -) |
| Distance formula |
d = √[(x₂ - x₁)² + (y₂ - y₁)²] |
| Midpoint formula |
[(x₁ + x₂)/2, (y₁ + y₂)/2] |
| Mirror image in x-axis |
(x, y) becomes (x, -y) |
| Mirror image in y-axis |
(x, y) becomes (-x, y) |