Question

Determine whether the given points are collinear
$A(0,2),B(1,-0.5),C(2,-3)$

Answer 1

$A(0,2)$, $B(1,-0.5)$, $C(2,-3)$
Three points are said to be collinear, if slope of any two pair of points is same.

Slope of a line $=\frac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1)$ and $(x_2,y_2)$ are its vertices

Slope of $AB=\frac{-0.5-2}{1-0}=-2.5$

Slope of $BC=\frac{-3-(-0.5)}{2-1}=-2.5$

So, the slope of $AB=$ slope of $BC$.
and Point $B$ lies on both the lines.
Hence, the given points are collinear.