Cartesian System and Distance Formula

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  • Q1

    Write the answer of each of the following questions:

    (i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

    (ii) Write the coordinates of the point where these two lines (as described above) intersect.

    Marks:2
    Answer:

    (i) To determine the position of any point in the Cartesian plane,
    (a) the horizontal line is called x- axis,
    (b) the vertical line is called y - axis
    (ii) The coordinates of the point where the axes intersect is (0, 0).

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  • Q2

    State in which quadrant do the following points lie.
    i. (3, -2)
    ii. (-2, 4)
    iii. (-5, 3)
    iv. (-3, -5)

    Marks:1
    Answer:

    i. Point (3, -2) lies in 4th quadrant.
    ii. Point (-2, 4) lies in 2nd quadrant.
    iii. Point (-5, 3) lies in 2nd quadrant.
    iv. Point (-3, -5) lies in 3rd quadrant.

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  • Q3

    Determine the quadrants in which the following points lie;
    (i) A (1,1)

    (ii) B (2,4)

    (iii) C (-3, -10)

    (iv) D (-1,2)

    (v) E (1,-1)

    (vi) F (-2,-4)


    Marks:3
    Answer:

    Quadrant I

    Quadrant II

    Quadrant III

    Quadrant IV

    Point A (1,1)

    Pont D (-1,2)

    Point C (-3,-10)

    Point E (1, -1)

    Point B (2,4)

    Point F (-2, -4)

    Both abscissa & ordinate +ve

    Abscissa is –ve & ordinate is +ve

    Both abscissa & ordinate are – ve

    Abscissa is +ve ordinate is -ve

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  • Q4

    Observe the fig. given below and answer the following:

    (i)The coordinates of B.

    (ii) The Coordinates of C.

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

    (iv)The abscissa of the point D.

    (v) The coordinates of H.

    Marks:2
    Answer:

    (i) Coordinates of B are (-5,2)
    (ii) Coordinates of C are (5,-5)
    (iii) Point identified by the coordinates (-3,-5) is E.
    (iv) Abscissa of the point D, x = 6
    (v) Coordinates of the point H are (-5,-3)

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  • Q5

    Plot the following points in a Cartesian plane:
    (-2,4), (3,-1), (-1, 0), (1, 2) & (-3, -5)

    Marks:3
    Answer:

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