Question

rectangle tuvw is on a coordinate plane at t (a, b), u (a + 2, b + 2), v (a + 5, b − 1), and w (a + 3, b − 3). what is the slope of the line that is parallel to the line that contains side wv? -2 2 -1 1

Explanation:

Step1: Recall slope formula

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

Step2: Identify points for side WV

Points are $W(a+3, b-3)$ and $V(a+5, b-1)$.

Step3: Calculate slope of WV

Substitute into slope formula:

$$\begin{align*} m_{WV}&=\frac{(b-1)-(b-3)}{(a+5)-(a+3)}\\ &=\frac{b-1-b+3}{a+5-a-3}\\ &=\frac{2}{2}\\ &=1 \end{align*}$$

Step4: Parallel lines have equal slopes

Slope of parallel line = slope of WV.

Answer:

1