Question

rectangle abcd is shown on the coordinate plane below. what is the perimeter of rectangle abcd? if necessary, round your answer to the nearest tenth. units

Explanation:

Step1: Determine the coordinates of the vertices

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

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

$x_1=-5,y_1 = 3,x_2=3,y_2 = 5$
$AB=\sqrt{(3 + 5)^2+(5 - 3)^2}=\sqrt{64 + 4}=\sqrt{68}=2\sqrt{17}\approx8.25$

Step3: Use the distance formula to find the length of $BC$

$x_1=3,y_1 = 5,x_2=4,y_2 = 1$
$BC=\sqrt{(4 - 3)^2+(1 - 5)^2}=\sqrt{1+16}=\sqrt{17}\approx4.12$

Step4: Calculate the perimeter of the rectangle

The perimeter $P = 2(AB + BC)$
$P=2(2\sqrt{17}+\sqrt{17})=2\times3\sqrt{17}=6\sqrt{17}\approx24.7$

Answer:

$24.7$