(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( , )