Question

He coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .

Answer 1

Answer: The perimeter is 17.52

Step-by-step explanation:

1. You can plot the points, as you can see in the graph attached.

2. As you can see in the graph, the points are:

$A(-2,-2)\\B(-2,3)\\C(2,4)\\D(3,1)\\E(0,-2)$

And the lenghts AB and EA are:

$AB=5$

$EA=2$

3. To find the other lenghts, you can apply the formula for calculate the distance between two points:

$distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

4. Thefore, you have:

$BC=\sqrt{(2-(-2))^{2}+(4-3)^{2}}=4.12\\CD=\sqrt{(2-3)^{2}+(4-1)^{2}}=3.16\\DE=\sqrt{(3-0)^{2}+(1-(-2))^{2}}=4.24$

5. The perimeter is:

$P=AB+CD+DE+EA\\P=5+4.12+3.16+4.24+2\\P=17.52$