Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also, find the coordinates of the point of division.

Let our points be A(5, -6) and B(-1, -4).

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 =

∴ m = 5n

∴ =

∴ m : n = 5 : 1

Now solving for y coordinate, with m = 5 and n = 1,

y =

y =

∴ y =

There is no need to solve for x, as our point lies on y-axis

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