The midpoint 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 value of y.

Explanation

The midpoint of `A B` is `(frac{-10-2}{2}, frac{4+10}{2})=P(-6,2)`.

Let `k` be the ratio in which `P` divides `C D`. So

`(-6,2)=(frac{k(-4)-9}{k+1}, frac{k(y)-4}{k+1})`

`Rightarrow frac{k(-4)-9}{k+1}=-6` and `frac{k(y)-4}{k+1}=2`

`Rightarrow k=frac{3}{2}`

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


`frac{y times frac{3}{2}-4}{frac{3}{2}+1}=2 `

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