Question

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

Answer 1

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

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

Let point (1, 3) divide the line segment joining (–1, 1) and (5, 7) in the ratio 1:k.
Accordingly, by section formula,

Thus, the line joining the points (–1, 1) and (5, 7) is divided by line x + y = 4 in the ratio 1:2.