Question

question 6 of 7, step 3 of 3
the following set of four ordered pairs below defines the vertices, in counter - clockwise order, of a quadrilateral (four - sided figure). {(-5, - 1), (0,0), (-1,4), (-6,3)}
step 3 of 3: determine if the quadrilateral is a parallelogram (a quadrilateral in which both pairs of opposite sides are parallel).

Explanation:

Step1: Recall the slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate the slopes of the four sides

Let $A=(-5,-1)$, $B=(0,0)$, $C=(-1,4)$, $D=(-6,3)$.
The slope of $AB$: $m_{AB}=\frac{0+1}{0 + 5}=\frac{1}{5}$.
The slope of $BC$: $m_{BC}=\frac{4 - 0}{-1-0}=-4$.
The slope of $CD$: $m_{CD}=\frac{3 - 4}{-6+1}=\frac{-1}{-5}=\frac{1}{5}$.
The slope of $DA$: $m_{DA}=\frac{-1 - 3}{-5+6}=\frac{-4}{1}=-4$.

Step3: Check for parallel sides

Since $m_{AB}=m_{CD}=\frac{1}{5}$ and $m_{BC}=m_{DA}=-4$, both pairs of opposite sides are parallel.

Answer:

Yes, the quadrilateral is a parallelogram.