Question

The mid point P of the line segment joining the points A (-10, 4) and B(-2, 0) lies on the line segment joining the points C (-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the values of y.

Answer 1

The midpoint of AB is $(\frac{-10-2}{2},\frac{4+0}{2})=P(-6,2)$

Let k:1 be the ratio in which P divides CD. So

$(-6,2)=(\frac{k(-4)-9}{k+1},\frac{k\left(y\right)-4}{k+1})$

⇒ $\frac{k(-4)-9}{k+1}=–6andy=\frac{k\left(y\right)-4}{k+1}$
⇒ $k=\frac{3}{2}$

Now, substituting $k=\frac{3}{2}$ in $\frac{k\left(y\right)-4}{k+1}=2$ we get

$(\frac{y\times \frac{3}{2}-4)}{(\frac{3}{2}+1)}=2$

⇒ $3y-\frac{8}{5}=2$
⇒ $y=\frac{(10+8)}{3}$
⇒y=6

Hence the required ratio is 3: 2 and y = 6