Question

I already did the graphing part I need help with finding the slopes and lengths.

Answer 1

Kindly check below.

1) Note that we need to find the slopes of the lines in order to classify that quadrilateral.

2) So, we need to find the slope of each line segment:

`\begin{gathered} m_(UV)=(y_2-y_1)/(x_2-x_1)=(-1-1)/(-2-(-5))=(-2)/(3)=-(2)/(3) \\ \\ m_(VW)=(2-(-1))/(3+2)=(3)/(5) \\ \\ m__(WX)=(4-2)/(1-3)=(2)/(-2)=-1 \\ \\ m_(XU)=(4-1)/(1-(-5))=(3)/(6)=(1)/(2) \end{gathered}`

3) Now, let's find the length of all sides as requested.

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ \\ d_(UV)=√((-2+5)^2+(-1-1)^2)=√(13)\approx3.6 \\ \\ d_(VW)=√((3+2)^2+(2+1)^2)=√(34)\approx5.8 \\ \\ d_(WX)=√((1-3)^2+(4-2)^2)=2√(2)\approx2.8 \\ \\ d_(XU)=√((-5-1)^2+(1-4)^2=)\:3√(5)\:\approx6.7 \end{gathered}`

4) Finally, we can tell that quadrilateral can be best identified as a parallelogram.