Question

Using the concept of slope, show that the points $A(5,-2),B(4,-1)$ and $C(1,2)$ are collinear.

Answer 1

Slope of the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$
Slope of the line $AB$ joining the points $A(5,-2)$ and $B(4-1)$ is $m_1=\frac{-1+2}{4-5}=-1$
Slope of the line $BC$ joining the points $B(4,-1)$ and $C(1,2)$ is $m_2=\frac{2+1}{1-4}=-1$
Thus, the slope of $AB=$ Slope of $BC$
Also, $B$ is the common point.
Hence, the points $A,B$ and $C$ are collinear.