Question

Show that the points $A(1,-2),B(3,6),C(5,10)$ and $D(3,2)$ are the vertices of a parallelogram.

Answer 1

Opposite sides of the parallelogram are parallel

It means the slope of the two sides are equal

Slope of line passing through two points$=\frac{y_2-y_1}{x_2-x_1}$

Consider, Sides AB and CD

$\therefore$$\frac{6+2}{3-1}=\frac{10-2}{5-3}$

$\frac{8}{2}=\frac{8}{2}$

Slope of $AB=$ Slope of $CD$

Slope of BC $=\left(\frac{10-6}{5-3}\right)=\frac{4}{2}$

Slope of AD $=\left(\frac{2+2}{3-1}\right)=\frac{4}{2}$

$\therefore$ The slope of BC=Slope of AD

Opposite sides are parallel. It means it is a parallelogram.