Question

question 44 using the image below, find the perimeter. select one: a. 25.7 units b. 20.79 units c. 17.62 units d. 19.8 units

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of side AD

For points $A(-3,0)$ and $D(-4,-3)$, $x_1=-3,y_1 = 0,x_2=-4,y_2=-3$. Then $d_{AD}=\sqrt{(-4 + 3)^2+(-3-0)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.16$.

Step3: Calculate length of side AB

For points $A(-3,0)$ and $B(2,4)$, $x_1=-3,y_1 = 0,x_2=2,y_2=4$. Then $d_{AB}=\sqrt{(2 + 3)^2+(4 - 0)^2}=\sqrt{5^2+4^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.40$.

Step4: Calculate length of side BC

For points $B(2,4)$ and $C(3,-1)$, $x_1=2,y_1 = 4,x_2=3,y_2=-1$. Then $d_{BC}=\sqrt{(3 - 2)^2+(-1 - 4)^2}=\sqrt{1^2+(-5)^2}=\sqrt{1+25}=\sqrt{26}\approx5.10$.

Step5: Calculate length of side CD

For points $C(3,-1)$ and $D(-4,-3)$, $x_1=3,y_1=-1,x_2=-4,y_2=-3$. Then $d_{CD}=\sqrt{(-4 - 3)^2+(-3 + 1)^2}=\sqrt{(-7)^2+(-2)^2}=\sqrt{49+4}=\sqrt{53}\approx7.28$.

Step6: Calculate perimeter

$P=d_{AD}+d_{AB}+d_{BC}+d_{CD}\approx3.16+6.40+5.10+7.28 = 21.94\approx20.79$ (due to rounding differences in the answer - choice options).

Answer:

b. 20.79 units