Question

consider parallelogram wxyz. note that wxyz has vertices w (-1,-1), x (5,-5), y (7,-2), and z (1,2). find the slope of segment xy. part 2 of 3 find the slope of a side adjacent to segment xy.

Explanation:

Step1: Recall slope formula

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

Step2: Identify points for segment XY

For segment $XY$, $X(5,-5)$ is $(x_1,y_1)$ and $Y(7,-2)$ is $(x_2,y_2)$.

Step3: Calculate slope of XY

$m_{XY}=\frac{-2-(-5)}{7 - 5}=\frac{-2 + 5}{2}=\frac{3}{2}$

Step4: Identify adjacent - side to XY

Adjacent sides to $XY$ are $WX$ and $YZ$. Let's find the slope of $WX$. For $W(-1,-1)$ as $(x_1,y_1)$ and $X(5,-5)$ as $(x_2,y_2)$.

Step5: Calculate slope of adjacent side (WX)

$m_{WX}=\frac{-5-(-1)}{5-(-1)}=\frac{-5 + 1}{5 + 1}=\frac{-4}{6}=-\frac{2}{3}$

Answer:

Part 1: $\frac{3}{2}$
Part 2: $-\frac{2}{3}$