In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

The equation of the line joining the points are (-1,1) and (5, 7) is given by

x – y + 2 = 0 ---------- (1)

The equation of the given line by

x + y – 4= 0 -----------(2)

The point of intersection of lines (1) and (2) is given by x = 1 and y = 3.

Let points (1,3) divide the line segment joining (-1,1) and (5,7) in the ratio 1: k.

Thus, by using section formula, we get,

Thus,

⇒ -k + 5 = 1+ k

⇒ 2k = 4

⇒ k = 2

Therefore, the line joining the points (-1, 1) and (5, 7) is divided by line

x + y = 4 in the ratio 1: 2.