Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by (i) x-axis (ii) y-axis. Also, find the coordinates of the point of division in each case.

(i) x-axis


(i) x-axis


Let our points be A(-2, -3) and B(5, 6).


Let point C(x, 0) divide the line formed by joining by the points A and B in ratio of m:n.



By section formula,


x = , y =


For point C(x, 0)


x = , 0 =


Solving for y coordinate,


0 =


∴ 6m -3n = 0


∴ 2m = n


∴ =


∴ m : n = 1 : 2


Now solving for x coordinate, with m = 1 and n = 2,


x =


∴ x=


∴ x =


Hence, the coordinates of required point is C( , 0)


(ii) y-axis.


Let our points be A(-2, -3) and B(5, 6).


Let point C(0, y) divide the line formed by joining by the points A and B in ratio of m:n.



By section formula,


x = , y =


For point C(0, y)


0 = , y =


Solving for x coordinate,


0 =


∴ 5m – 2n = 0


∴ =


∴ m : n = 2 : 5


Now solving for y coordinate, with m = 2 and n = 5,


y =


y =


∴ y =


Hence, the coordinates of required point is C( , )


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