Question

7) The coordinates of the vertices of a polygon are (-4,-1), 1-2, -3), (1, 3), (1, 1), (3, 2).Find the perimeter of the polygon to the nearest 10th.Show all of your work including the length of each side of the polygon. (1.5 points)

Answer 1

`\begin{gathered} \text{The distance betw}een\text{ two vertioces is,} \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ So\text{ the distance betwen (}-4,-1)\text{ and (}-2,-3) \\ d_1=\sqrt[]{(-2+4)^2+(-3+1)^2}=\sqrt[]{2^2+2^2}=2.828 \\ So\text{ the distance betwen (}-2,-3)\text{ and (1},-3) \\ d_2=\sqrt[]{(1+2)^2+(-3+3)^2}=\sqrt[]{3^2+0^2}=3 \\ So\text{ the distance betwen (1},-3)\text{ and (1},1) \\ d_3=\sqrt[]{(1-1)^2+(1+3)^2}=\sqrt[]{0^2+4^2}=4 \\ So\text{ the distance betwen (1},1)\text{ and (-3},2) \\ d_4=\sqrt[]{(-3-1)^2+(2-1)^2}=\sqrt[]{(-4)^2+1^2}=4.123 \\ So\text{ the distance betwen (-3},2)\text{ and }(-4,-1) \\ d_5=\sqrt[]{(-4+_{}3)^2+(-1-2)^2}=\sqrt[]{(1)^2+(-3)^2}=3.16 \\ \text{Perimeter}\Rightarrow d_1+d_2+d_3+d_4+d_5 \\ \text{perimeter}=2.828+3+4+4.123+3.16 \\ \text{perimeter}=17.11 \end{gathered}`