Question

maya is setting up a tent for a school camping trip. she marks four stakes in the ground at the following points: point w (1,3) point x (5,3) point y (-1,7) point z (2,6) she connects them in this order to form a closed four - sided layout: w - x - y - z - w maya says, \im sure one corner is exactly 90°, but the rest feel a little tilted.\ which corner is she referring to? a corner y b corner z c corner w d corner x

Explanation:

Step1: Calculate slopes of adjacent sides

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Slope of $WX$: $m_{WX}=\frac{3 - 3}{5 - 1}=0$.
Slope of $XY$: $m_{XY}=\frac{7 - 3}{- 1-5}=-\frac{2}{3}$.
Slope of $YZ$: $m_{YZ}=\frac{6 - 7}{2+1}=-\frac{1}{3}$.
Slope of $ZW$: $m_{ZW}=\frac{3 - 6}{1 - 2}=3$.

Step2: Check perpendicularity

Two lines are perpendicular if the product of their slopes is - 1.
For $ZW$ and $WX$, $m_{ZW}\times m_{WX}=3\times0 = 0
eq - 1$.
For $WX$ and $XY$, $m_{WX}\times m_{XY}=0\times(-\frac{2}{3}) = 0
eq - 1$.
For $XY$ and $YZ$, $m_{XY}\times m_{YZ}=(-\frac{2}{3})\times(-\frac{1}{3})=\frac{2}{9}
eq - 1$.
For $YZ$ and $ZW$, $m_{YZ}\times m_{ZW}=(-\frac{1}{3})\times3=-1$.
The corner where $YZ$ and $ZW$ meet is corner $Z$.

Answer:

B. corner Z