Question

A(12, 2), B(16, 4), C(18, 8), D(14, 6) are the vertices of a parallelogram.

• A. True
• B. False

Answer 1

The correct option is A

True

A quadrilateral $ABCD$ is a parallelogram if $AB$ is parallel to $CD$ and $BC$ is parallel to $CA$.

The slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2-y_1}{x_2-x_1}$.

Given A(12, 2), B(16, 4), C(18, 8), D(14, 6)

The slope of $AB=\frac{4-2}{16-12}=\frac{1}{2}$

The slope of $BC=\frac{8-4}{18-16}=2$

The slope of $CD=\frac{6-8}{14-18}=\frac{1}{2}$

The slope of $DA=\frac{2-6}{12-14}=2$

Slope of $AB=CD$ and $BC=DA$, therefore $ABCD$ is a paralleogram.