Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3)

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find m.

Answer

Let AP : PB = k : 1

$$ \frac{6k +2}{k + 1} = 4 $$

k = 1, ratio is 1 : 1 

$$ m = \frac{-3 + 3}{2} = 0 $$