Question

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.

Answer 1

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,

Solving for x coordinate,

0 = \(\frac{m\times(-1)+n\times5}{m+n}\)

∴ m = 5n

∴ \(\frac{m}n\) = \(\frac{5}1\)

∴ m : n = 5 : 1 

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

y = \(\frac{my_2+ny_1}{m+n}\)

y = \(\frac{-4\times5-6}{6}\)

∴ y = \(\frac{-13}6\)

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

Hence, the coordinates of required point is C( 0,\(\frac{-13}6\))