Question

If (x, y) be on the line joining the two points (1, –3) and (–4, 2), prove that x + y + 2 = 0.

Answer 1

Since the point (x, y) lie on the line joining the points (1, −3) and (−4, 2); the area of triangle formed by these points is 0.

That is,

Δ `= 1/2 { x (- 3 -2 ) + 1 (2 - y ) - 4 (y + 3) } = 0`

- 5x + 2 - y - 4y - 12 = 0

- 5x - 5y - 10 = 0

x + y + 2 = 0

Thus, the result is proved.