Question

Using slopes, prove that the points $A(-2,-1),B(1,0),C(4,3)$ and $D(1,2)$ are the vertices of a parallelogram.

Answer 1

Given points :- $A\equiv (-2,-1)$

$B\equiv (1,0),C\equiv (4,3)$ and $D\equiv (1,2)$

Slope of $AB=\frac{0-(-1)}{1-(-2)}$

$=\frac{1}{3}----\left(1\right)$

slope of $CD=\frac{2-3}{1-4}$

$=\frac{-1}{-3}=\frac{1}{3}-----\left(2\right)$

$\therefore$ From $\left(1\right)$ & $\left(2\right)$

Slope of $AB=$ slope of $CD$

Hence $A,B,C$ and $D$ are vertices of parallelogram.