Chapter 3 - Coordinate Geometry, Solved Examples, Class 9, Maths | Mathematics for GCSE/IGCSE - Class 10 PDF Download

Ex 1. Find the distance between the points P(3, 2) and Q(-4, 5)

Sol. P(3, 2), Q(-4, 5)

Ex 2. Find the point on the x-axis which is equidistance from (2, -5) and (-2, 9).
 Sol. We know that a point on the x-axis is of form (x, 0). Let the point on the x-axis be P(x, 0) and the given points are A(2, -5) and B(-2, 9)

Ex 3. In which quadrant do the following points lie ?
 (i) (3, 2) 

(ii) (-2, 1) 

(iii) (-1, -3) 

(iv) (5, -1)
 

Sol. (i) In the point (3, 2) abscissa and ordinate one both positive. So it lies in the 1st quadrant.
(ii) In the point (-2, 1) abscissa is negative and ordinate is positive. So it lies in the second quadrant.
(iii) In the point (-1, -3) abscissa and ordinate are both negative. So it lies in third quadrant.
(iv)In the point (5, -1) abscissa is positive and ordinate is negative. So it ies in the fourth quadrant.

Ex 4. Which of the following points lie on the x-axis.
 (i) (1, 1) 

(ii) (1, 0) 

(iii) (0, 1) 

(iv) (0, 0)
 (v) (-1, 0) 

(vi) (0, -1) 

(vii) (4, 0) 

(viii) (0, -7)
 Sol. Points of the form (a, 0),i.e. the points in which ordinate is 0, those points lie on the x-axis, and the points in which abscissa is 0, lie on the y-axis.

(ii) (1, 0),

(iv) (0, 0),

(v) (-1, 0),

(vii) (4, 0).

Ex 5. Plot the following points on the graph paper.
 (i) A(2, 5) 

(ii) B(-5, -7) 

(iii) C(3, -2) 

(iv) D(0, 5)
 (v) E(5, 0)

Sol. Let XOX' and YOY' be the coordinate axes. Then the given points may be plotted as given below :-

Ex 6. Plot the following points on a graph paper.
 (i) (3, 4) 

(ii) (-2, 3) 

(iii) (-5, -2) (iv) (4, -3)
 Sol. Let X'OX and Y'OY be the coordinate axes. The given four points may be potted as given below:

Ex 7. From the figure, find :
 (i) Absicca
 (ii) Ordinate
 (iii) Co-ordinate of point P.

Sol. (i) Abscissa = PN = OM = 3 units
(ii) Ordinate = PM =ON = 4 units
(iii) Co-oridinate of the point P = (Abscissa, ordinate) = (3, 4)

Ex 8. Determine y
 (i) Abscissa N
 (ii) Ordinate
 (iii) Co-ordinate of point P given in the following figure.

Sol. (i) Abscissa of the point P = -NP = -OM = - a
(ii) Ordinates of the point P = MP = ON = b
(iii) Co-ordinates of the point P = (Abscissa, ordinate) = (-a, b)

Ex 9. Write down the
 (i) Absicca
 (ii) Ordinate
 (iii) Co-ordinate of P, Q, R and S as given in figure :


Sol. Point P : Abscissa of P = 2 ; Ordinate of P = 3
Co-ordinate of P = (2, 3)
Point Q : Abscissa of Q = -2 ; Ordinate of Q = 4
Co-ordinate of Q = (-2, 4)
Point R : Abscissa of R = -5 ; Ordinate of R = -3
Co-ordinate of R = (-5, -3)
Point S : Abscissa of S = 5 ; Ordinate of S = -1
Co-ordinate of S = (5, -1)

Ex 10. Plot the points A(2, 0), B(2, 2), C(0, 2) and draw the line segment OA, AB, BC and CO. What figure do you obtain ?

Sol. On joining OA, AB, BC and CO, we get a square of each side 2 units.