Question

The coordinates of the vertices of a polygon are (−5, 1) , (−1, 3) , (2, 3) , (2, −2) , and (−3, −1) .

Answer 1

Using the distance formula $d=\sqrt{(x_2-x_1) +(y_2-y_1) }$   Then we assign the points letter for simplicity

$A= (-5.1),B=(-1,3),C=(2,3),D=(2,-2),E=(-3,-1)$. The distance formula gives us the magnitude between two points hence,

$AB=\sqrt{(-5-(-1))^2+ (-1-3)^2}=\sqrt{16+16}= 5.65$

$BC=\sqrt{(-1-2)^2+(3-3)^2}= \sqrt{9}=3$

$CD=\sqrt{(2-2)^2+((3-(-2))^2} =\sqrt{25}=5$

$DE=\sqrt{(2-(-3))^2+(-2-(-1))^2} =\sqrt{26+1} =5.099$

$AE=\sqrt{(-3-(-5))^2+(-1-1)^2}= \sqrt{4+4} =\sqrt{8}=2.82$

$Perimeter= AB+BC+CD+DE+AE\\Perimeter=5.65+3+5+5.099+2.82=21.57 units$