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{w u}) is (square).
the slope of (overline{v u}) is (square).
therefore, (angle u) is (square).

Explanation:

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

Given \( W(0,1) \) and \( U(2,4) \), using the slope formula \( m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \).
\( m_{WU}=\frac{4 - 1}{2-0}=\frac{3}{2} \)

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

Given \( V(5,2) \) and \( U(2,4) \), using the slope formula \( m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \).
\( m_{VU}=\frac{4 - 2}{2 - 5}=\frac{2}{-3}=-\frac{2}{3} \)

Step3: Determine the nature of \( \angle U \)

If two lines with slopes \( m_1 \) and \( m_2 \) are perpendicular, then \( m_1\times m_2=- 1 \).
Here, \( m_{WU}\times m_{VU}=\frac{3}{2}\times(-\frac{2}{3})=-1 \). So, \( \overline{WU}\perp\overline{VU} \), and \( \angle U = 90^{\circ} \) (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.