Question

Determine the ratio in which the point P (m, 6) divides the join A (-4, 3) and B (2, 8), also find the value of m.

Answer 1

Let the ratio in which the point P divides the line segment joining the points A(-4, 3) and B(2, 8) be 1:k.
Y-coordinate of point P:
$\frac{8+3k}{1+k}=6$

By cross multiplication,
$\Rightarrow$ 8 + 3k = 6 + 6k
$\Rightarrow$ 3k = 2
$\Rightarrow$ k = 2/3
So, the ratio in which the point divides AB = 1 : 2/3 = 3 : 2
X-coordinate of P:
$\frac{6-8}{3+2}=m$
By cross multiplication,$\Rightarrow$ 6 - 8 = 5m

$\Rightarrow$ m = $\frac{-2}{5}$
Hence, the value of m is -2/5