Question

follow these steps to prove the given quadrilateral is a parallelogram.
√ 1. determine the slope of ab: 4/3
√ 2. determine the slope of dc: 4/3
√ 3. determine the length of ab: 5

1. determine the length of dc:

Explanation:

Step1: Recall distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Since $AB$ and $DC$ are parallel (same slope $\frac{4}{3}$) and we know the length of $AB = 5$. In a parallelogram, opposite - sides are equal.

Step2: Determine length of $DC$

Since opposite sides of a parallelogram are equal, and $AB$ and $DC$ are opposite sides, the length of $DC$ is the same as the length of $AB$.

Answer:

5