Question

The line joining (-1. 1) and (5, 7) is divided by the line x+y=4 in the ratio 1: k. The value of k' is​

Answer 1

Step-by-step explanation:

Suppose the line x+y=4 divides the join of A(−1,1) and B(5,7) in the ratio λ:1.

The coordinates of the point of division are (λ+15λ+1,λ+17λ+1). It lies on x+y=4.

Therefore,

λ+15λ−1+λ+17λ+1=4

5λ−1+7λ+1=4(λ+1)

12λ=4λ+4

8λ=4

λ=21

Hence, the required ratio is 1:2.