Question

prove that the diagonals of kite uvwx are perpendicular. step 1: determine the slope of xv. the slope of xv is blank. step 2 determine the slope of uw. the slope of uw is blank. step 3 the slopes of the diagonals are blank. the diagonals of kite uvwx are congruent, parallel, perpendicular

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Assume the coordinates of $X(x_1,y_1)$ and $V(x_2,y_2)$. From the graph, if we assume $X(-1,-1)$ and $V(5,3)$. Then the slope of $\overline{XV}$ is $m_{XV}=\frac{3+1}{5 + 1}=\frac{4}{6}=\frac{2}{3}$.

Step2: Determine slope of $\overline{UW}$

Assume the coordinates of $U(-2,5)$ and $W(4,-3)$. Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_{UW}=\frac{-3 - 5}{4+2}=\frac{-8}{6}=-\frac{4}{3}$.

Step3: Check the relationship between slopes

Two non - vertical lines with slopes $m_1$ and $m_2$ are perpendicular if $m_1\times m_2=-1$. Here, $m_{XV}\times m_{UW}=\frac{2}{3}\times(-\frac{3}{2})=-1$.

Answer:

The slope of $\overline{XV}$ is $\frac{2}{3}$, the slope of $\overline{UW}$ is $-\frac{3}{2}$, the slopes of the diagonals are negative reciprocals, the diagonals of kite $UVWX$ are perpendicular.