Let the line joining A(–1, 1) and B(5, 7) is divided by the line x + y = 4 and meet the AB at C, such that C divides the line segment AB in the ratio λ : 1.

∴ C = (

5λ−1

λ+1

,

7λ+1

λ+1

)
But C lies on the line x + y = 4
⇒

5λ−1

λ+1

+

7λ+1

λ+1

= 4
⇒ 5λ - 1 + 7λ + 1 = 4 (λ + 1)
⇒ 12λ = 51 + 4 ⇒ 8λ = 4 ⇒ λ =

1

2

Hence, the required ratio is 1 : 2.