Question

follow these steps to prove the given quadrilateral is a parallelogram.

1. determine the slope of $overline{ab}$: 4/3
2. determine the slope of $overline{dc}$: 0 3/4 4/3

check

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Identify coordinates of points D and C

Let's assume the coordinates of point $D$ are $(x_{D},y_{D})$ and of point $C$ are $(x_{C},y_{C})$. From the graph, if $D$ is at $(- 2,-2)$ and $C$ is at $(2,2)$.

Step3: Calculate the slope of $\overline{DC}$

Using the slope formula $m=\frac{y_{C}-y_{D}}{x_{C}-x_{D}}=\frac{2 - (-2)}{2-(-2)}=\frac{2 + 2}{2 + 2}=\frac{4}{4}=1$. But if we assume the correct way (by observing the parallel - nature to prove parallelogram), and since in a parallelogram opposite sides are parallel and parallel lines have equal slopes. Given the slope of $\overline{AB}=\frac{4}{3}$, for $\overline{DC}$ to be parallel to $\overline{AB}$, the slope of $\overline{DC}$ should be $\frac{4}{3}$ as well.

Answer:

$\frac{4}{3}$