Given the points, we graph it as follows:
A. We determine the lengths of each side using the following expression:
[tex]d=\sqrt[]{(X)^2+(Y)^2_{}}[/tex]
Here X & Y are the x & y-components from the directional vectors made from the points given.
Now, using the points we find the following directional directional vectors:
[tex]RA=(3-7,-6+1)\Rightarrow RA=(-4,-5)[/tex][tex]AB=(-3-3,-6+6)\Rightarrow AB=(-6,0)[/tex][tex]BE=(-3+5,-6-4)\Rightarrow BE=(2,-10)[/tex][tex]RE=(-5-7,4+1)\Rightarrow RE=(-12,5)[/tex]
Now, we will determine the lengths of each side:
[tex]d_{RA}=\sqrt[]{(-4)^2+(-5)^2}\Rightarrow d_{RA}=\sqrt[]{41}[/tex][tex]d_{AB}=\sqrt[]{(-6)^2+(0)^2}\Rightarrow d_{AB}=6[/tex][tex]d_{BE}=\sqrt[]{2^2+(-10)^2}\Rightarrow d_{BE}=2\sqrt[]{26}[/tex][tex]d_{RE}=\sqrt[]{(-12)^2+5^2}\Rightarrow d_{RE}=13[/tex]
So, the lengths of each side are:
Side RA = 6.40 units.
Side AB = 6 units.
Side BE = 10.20 units.
Side RE = 13 units.
B. The approximate perimeter is:
6.40 + 6 + 10.20 + 13 = 55.4
So, its perimeter is approximately 55.4 units.
