Question

By using the concept of equation of a line, prove that the three points (3, 0), (- 2, - 2) and (8, 2) are collinear.

Answer 1

In order to show that points (3, 0), (-2, -2), and (8, 2) are collinear, it suffices to show that the line passing through points (3, 0) and (-2, -2) also passes through point (8, 2).

The equation of the line passing through points (3, 0) and (-2, -2) is
$(y-0)=\frac{(-2-0)}{(-2-3)}(x-3)$

$y=\frac{-2}{-5}(x-3)$

$5y=2x-6$

$i.e,2x-5y=6.$

It is observed that at $x = 8$ and $y = 2$,
$L.H.S. = 2 × 8 \- 5 × 2 = 16 -10 = 6 = R.H.S.$
Therefore, the line passing through points (3, 0) and (-2, -2) also passes through point (8, 2). Hence, points (3, 0), (-2, -2), and (8, 2) are collinear.