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 .

Answer 1

Hello dear,
Given points are A(-10, 4) and B(-2, 0)

P is mid point of AB =  -10-2 2 4+0 2 = [-6, 2]

Let the ratio m:n and points C(-9,-4) D(-4,y).

P divides the CD in the ratio m:n then  -4m - 9n m+n, my - 4n m + n = (-6, 2)

equating co-ordinates on both sides we get

- 4m - 9n m+n = -6 

⇒ -4m - 9n = -6m - 6n

⇒  3m = 3n

  ⇒  m n = 3 2 ----------(1)

Now my - 4n = 2(m+n)

 ⇒ m(y - 2) = 6n

⇒  m n = y - 2 6 

⇒   3 2 = y - 2 6 

⇒  y - 2 = 9

  ∴ y = 11.

I hope you understand very well dear :-)