Question

the coordinates of the vertices of a polygon are $(-2, -2)$, $(3, -3)$, $(4, -6)$, $(1, -6)$, and $(-2, -4)$. what is the perimeter of the polygon to the nearest tenth of a unit? 15.3 units 16.9 units 17.5 units 17.9 units

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For points \((-2,-2)\) and \((3,-3)\):
\(d_1=\sqrt{(3 + 2)^2+(-3 + 2)^2}=\sqrt{25 + 1}=\sqrt{26}\approx5.1\)

Step2: For points \((3,-3)\) and \((4,-6)\)

\(d_2=\sqrt{(4 - 3)^2+(-6 + 3)^2}=\sqrt{1+9}=\sqrt{10}\approx3.2\)

Step3: For points \((4,-6)\) and \((1,-6)\)

\(d_3=\sqrt{(1 - 4)^2+(-6+6)^2}=\sqrt{9 + 0}=3\)

Step4: For points \((1,-6)\) and \((-2,-4)\)

\(d_4=\sqrt{(-2 - 1)^2+(-4 + 6)^2}=\sqrt{9+4}=\sqrt{13}\approx3.6\)

Step5: For points \((-2,-4)\) and \((-2,-2)\)

\(d_5=\sqrt{(-2+2)^2+(-2 + 4)^2}=\sqrt{0 + 4}=2\)

Step6: Sum up the distances

Perimeter \(P=d_1 + d_2+d_3+d_4+d_5\approx5.1+3.2 + 3+3.6+2=16.9\)

Answer:

16.9 units