Respuesta :
Let
A(3,6) B(0,-2) C(-7,-5) D(-4,3)
Remember that
A parallelogram has opposite sides congruent and parallel
so
step 1
Find out the length of the side AB
using the formula to calculate the distance between two points
[tex]\begin{gathered} AB=\sqrt{(-2-6)^2+(0-3)^2} \\ AB=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side AB
[tex]m_{AB}=\frac{-2-6}{0-3}=\frac{8}{3}[/tex]step 2
Find out the length of the side BC
[tex]\begin{gathered} BC=\sqrt{(-5+2)^2+(-7-0)} \\ BC=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side BC
[tex]m_{BC}=\frac{-5+2}{-7-0}=\frac{3}{7}[/tex]step 3
Find out the length of the side CD
[tex]\begin{gathered} CD=\sqrt{(3+5)^2+(-4+7)^2} \\ CD=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side CD
[tex]m_{CD}=\frac{3+5}{-4+7}=\frac{8}{3}[/tex]step 4
Find out the length of the side AD
[tex]\begin{gathered} AD=\sqrt{(3-6)^2+(-4-3)^2} \\ AD=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side AD
[tex]m_{AD}=\frac{3-6}{-4-3}=\frac{3}{7}[/tex]step 5
Compare the length of the sides
we have that
AB=CD
BC=AD
that means ----> opposite sides are congruent
Compare their slopes
mAB=mCD
mBC=mAD
that means ----> opposite sides are parallel
therefore
