Question

Show that the following points are collinear.

(4, 1), (5, -2) and (6, -5)

Answer 1

$A(4,1)$

$B(5,-2)$

$C(6,-5)$

Slope of $(x_1,y_1),(x_2,y_2)$

$=\frac{y_2-y_1}{x_2-x_1}$

$m_{AB}=\frac{-2-1}{5-4}=-3$

$m_{BC}=\frac{-5-(-2)}{6-5}=-3$

Hence they are collinear.