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 = $\left(\frac{5\lambda-1}{\lambda+1},\frac{7\lambda+1}{\lambda+1}\right)$ But C lies on the line x + y = 4 ⇒ $\frac{5\lambda-1}{\lambda+1} + \frac{7\lambda+1}{\lambda+1}$ = 4 ⇒ 5λ - 1 + 7λ + 1 = 4 (λ + 1) ⇒ 12λ = 51 + 4 ⇒ 8λ = 4 ⇒ λ = $\frac{1}{2}$ Hence, the required ratio is 1 : 2.