Question

find the ratio in which the line y-x+2=0 divides the join of (3 -1) and (8,9)

Answer 1

Suppose the line (x – y – 2 = 0) divides the line segment Joining A (3, – 1) and B (8, 9) in the ratio K : 1 at point C. Then the coordinates of C are
8k+3/k+1 ,9k-1/k+1

But C lies on (x + y – 2 = 0). Therefore,

8k+3/k+1 =9k-1/k+1 - 2 =0
8k+3 -9k+1 - 2(k+1) / k+1 =0

⇒ – K + 4 – 2K – 2 = 0

⇒ – 3K + 2 = 0

k=2/3

So, the required ratio is 2 : 3 internally.