Using the distance formula;[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We find the length of each side of the parallelogram as follows:
Side JK
[tex]|JK|=\sqrt{(3--3)^2+(9-9)^2}[/tex]
[tex]|JK|=\sqrt{(3+3)^2+(0)^2}[/tex]
[tex]|JK|=\sqrt{(6)^2+(0)^2}[/tex]
[tex]|JK|=\sqrt{(6)^2+(0)^2}[/tex]
[tex]|JK|=\sqrt{(6)^2+0}[/tex]
[tex]|JK|=\sqrt{(6)^2}[/tex]
[tex]|JK|=\sqrt{(6)^2}=6[/tex] units
Side KL
[tex]|KL|=\sqrt{(1-3)^2+(1-9)^2}[/tex]
[tex]|KL|=\sqrt{(-2)^2+(-8)^2}[/tex]
[tex]|KL|=\sqrt{4+64}[/tex]
[tex]|KL|=\sqrt{68}[/tex]
[tex]|KL|=8.25[/tex] units
Side LM
[tex]|LM|=\sqrt{(-5-1)^2+(1-1)^2}[/tex]
[tex]|LM|=\sqrt{(-6)^2+(0)^2}[/tex]
[tex]|LM|=\sqrt{36}[/tex]
[tex]|LM|=6[/tex] units
Side MJ
[tex]|MJ|=\sqrt{(-3--5)^2+(9-1)^2}[/tex]
[tex]|MJ|=\sqrt{(-3+5)^2+(9-1)^2}[/tex]
[tex]|MJ|=\sqrt{(2)^2+(8)^2}[/tex]
[tex]|MJ|=\sqrt{4+64}[/tex]
[tex]|MJ|=\sqrt{68}[/tex]
[tex]|MJ|=8.25[/tex] units.
We can see that
[tex]|JK|=|ML|=6[/tex] units
[tex]|MJ|=|LK|=8.25[/tex] units .
Since the opposite sides are equal, they are congruent.
See diagram
