Question

find the perimeter of the quadrilateral. round to the nearest tenth if necessary.
(-2,2)
(2,2)
(-4,-2)
(4,-2)

a. 12
b. 16.5
c. 21
d. 24

Explanation:

Step1: Find length of top - side

The two endpoints of the top - side are $(- 2,2)$ and $(2,2)$. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, since $y_1 = y_2=2$, the length $d_1=\vert2-( - 2)\vert=4$.

Step2: Find length of bottom - side

The two endpoints of the bottom - side are $(-4,-2)$ and $(4,-2)$. Since $y_1 = y_2=-2$, the length $d_2=\vert4-( - 4)\vert = 8$.

Step3: Find length of left - side

The endpoints of the left - side are $(-4,-2)$ and $(-2,2)$. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $x_1=-4,y_1 = - 2,x_2=-2,y_2 = 2$. Then $d_3=\sqrt{(-2+4)^2+(2 + 2)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.5$.

Step4: Find length of right - side

The endpoints of the right - side are $(2,2)$ and $(4,-2)$. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $x_1 = 2,y_1=2,x_2 = 4,y_2=-2$. Then $d_4=\sqrt{(4 - 2)^2+(-2 - 2)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.5$.

Step5: Calculate perimeter

The perimeter $P=d_1 + d_2+d_3 + d_4=4 + 8+4.5+4.5 = 21$.

Answer:

C. 21