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