Question

which best describes the figure that is represented by the following coordinates? a(-4,3), b(2,3), c(3,-1) and d(-5,-1)

Explanation:

Step1: Calculate slope of AB

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-4,3)$ and $B(2,3)$, $m_{AB}=\frac{3 - 3}{2-(-4)} = 0$.

Step2: Calculate slope of CD

For points $C(3,-1)$ and $D(-5,-1)$, $m_{CD}=\frac{-1-(-1)}{-5 - 3}=0$.

Step3: Calculate slope of BC

For points $B(2,3)$ and $C(3,-1)$, $m_{BC}=\frac{-1 - 3}{3 - 2}=-4$.

Step4: Calculate slope of AD

For points $A(-4,3)$ and $D(-5,-1)$, $m_{AD}=\frac{-1 - 3}{-5-(-4)} = 4$.
Since $m_{AB}=m_{CD}$ and $m_{BC}
eq m_{AD}$, one - pair of opposite sides is parallel, so the figure is a parallelogram.

Answer:

A. a parallelogram