Question

Points A(1, 1), B(2, 2), C(3, 3) and D(4, 4) form a parallelogram.

• A. True
• B. False

Answer 1

The correct option is B

False

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(1, 1), B(2, 2), C(3, 3), D(4, 4)

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

The slope of $BC=\frac{3-2}{3-2}=1$

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

The slope of $DA=\frac{1-4}{1-4}=1$

In this case the slope of all line are equla, ie. they do not form a paralleogram. They from a straight line.