Question

Uses slopes to determine whether the opposite sides of quadrilateral WXYZ are parallel.

Answer 1

the sides of the quadrilateral WXYZ are NOT parallel

Explanation

two segments are parallel if the slope is the same .so

the slope of a line ( or segment) is given by

$\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1)\text{ is the initial point} \\ \text{and} \\ P2(x_2,y_2)\text{ is the endpoint} \end{gathered}$

Step 1

so, let's find the slopes of the sides

a)WX

let

W=P1(-1,-1)

X=P2(-3,-1)

now, replace in the formula

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_{_{WX}}=\frac{-1-(-1)}{-3-(-1)}=\frac{-1+1}{-2}=\frac{0}{-2}=0 \\ slope_{_{WX}}=0 \end{gathered}$

b)XY

let

X=P1(-3,-1)

Y=P2(-2,4)

now, replace in the formula

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_{_{XY}}=\frac{4-(-1)}{-2-(-3)}=\frac{5}{1}=5 \\ slope_{_{XY}}=0 \end{gathered}$

c)YZ

let

Y=P1(-2,4)

Z=P2(2,3)

now, replace in the formula

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_{_{YZ}}=\frac{3-4}{2-(-2)}=\frac{-1}{2+2} \\ slope_{_{YZ}}=-\frac{1}{4} \end{gathered}$

d)ZW

let

Z=P1(2,3)

W=P2(-1,-1)

now, replace in the formula

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_{_{Zw}}=\frac{-1-3}{-1-2}=\frac{-4}{-3}=\frac{4}{3} \\ slope_{_{ZW}}=\frac{4}{3} \end{gathered}$

conclusion: two lines ( or segments are parellale if the slope is the same), here we found that the 4 slopes are differentes, so the sides of the quadrilateral WXYZ are NOT parallel

I hope this helps you