Question

1. show that the included angles, $\angle j$ and $\angle v$, are congruent right angles.

slope $=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
the slope of $\overline{wu}$ is.
the slope of $\overline{vu}$ is.
therefore, $\angle u$ is.

Explanation:

Step1: Calculate the slope of \( \overline{WU} \)

Given \( W(0,1) \) and \( U(2,4) \).
Using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \), we have \( m_{WU}=\frac{4 - 1}{2 - 0}=\frac{3}{2} \).

Step2: Calculate the slope of \( \overline{VU} \)

Given \( V(5,2) \) and \( U(2,4) \).
Using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \), we have \( m_{VU}=\frac{4 - 2}{2 - 5}=\frac{2}{-3}=-\frac{2}{3} \).

Step3: Check the relationship between the slopes

If two lines are perpendicular, the product of their slopes is \( - 1 \).
\( m_{WU}\times m_{VU}=\frac{3}{2}\times(-\frac{2}{3})=-1 \). So, \( \angle U \) is a right angle.

Answer:

The slope of \( \overline{WU} \) is \( \frac{3}{2} \). The slope of \( \overline{VU} \) is \( -\frac{2}{3} \). Therefore, \( \angle U \) is a right angle.