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

The equation of the line passing through points $(3,0)$ and $(-2,-2)$ is

$(y-0)=\frac{(-2-0)}{(-2-3)}(x-3)$

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

$\Rightarrow 2x-5y=\mathrm{6......}\left(1\right)$

It is observed that point $(8,2)$ also satisfying eqn. (1)

$\Rightarrow 2\left(8\right)-5\left(2\right)=16-10=6$

Hence given points are collinear.