Question

select the correct answer.
consider polygon abcde on the coordinate grid.
what is the best approximation for the perimeter of polygon abcde?
a. 24.3 units
b. 22.1 units
c. 11.0 units
d. 17.0 units

Explanation:

Step1: Find the coordinates of each vertex

$A(-1,3)$, $B(0,6)$, $C(5,4)$, $D(4,0)$, $E(-1,-1)$

Step2: Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

• For $AB$: $x_1=-1,y_1 = 3,x_2=0,y_2 = 6$

$AB=\sqrt{(0 - (-1))^2+(6 - 3)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.16$

• For $BC$: $x_1=0,y_1 = 6,x_2=5,y_2 = 4$

$BC=\sqrt{(5 - 0)^2+(4 - 6)^2}=\sqrt{25+4}=\sqrt{29}\approx5.39$

• For $CD$: $x_1=5,y_1 = 4,x_2=4,y_2 = 0$

$CD=\sqrt{(4 - 5)^2+(0 - 4)^2}=\sqrt{1 + 16}=\sqrt{17}\approx4.12$

• For $DE$: $x_1=4,y_1 = 0,x_2=-1,y_2 = -1$

$DE=\sqrt{(-1 - 4)^2+(-1 - 0)^2}=\sqrt{25 + 1}=\sqrt{26}\approx5.10$

• For $EA$: $x_1=-1,y_1 = -1,x_2=-1,y_2 = 3$

$EA=\sqrt{(-1-(-1))^2+(3 - (-1))^2}=\sqrt{0 + 16}=4$

Step3: Calculate the perimeter $P=AB + BC+CD + DE+EA$

$P\approx3.16+5.39+4.12+5.10+4=21.77\approx22.1$

Answer:

B. 22.1 units