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

Step-by-step 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}=(\Delta y)/(\Delta x)=(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}=(y_2-y_1)/(x_2-x_1) \\ slope_{_(WX)}=(-1-(-1))/(-3-(-1))=(-1+1)/(-2)=(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}=(y_2-y_1)/(x_2-x_1) \\ slope_{_(XY)}=(4-(-1))/(-2-(-3))=(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}=(y_2-y_1)/(x_2-x_1) \\ slope_{_(YZ)}=(3-4)/(2-(-2))=(-1)/(2+2) \\ slope_{_(YZ)}=-(1)/(4) \end{gathered}`

d)ZW

let

Z=P1(2,3)

W=P2(-1,-1)

now, replace in the formula

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ slope_{_(Zw)}=(-1-3)/(-1-2)=(-4)/(-3)=(4)/(3) \\ slope_{_(ZW)}=(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