Question

what is the perimeter of rectangle efgh? g(-3, 4) h(2, 2) f(-4, 1) e(1, -1) 22 units 39 units 2√10 + 2√29 units √10 + √29 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 EF

For points $E(1,-1)$ and $F(-4,1)$, $x_1 = 1,y_1=-1,x_2=-4,y_2 = 1$. Then $EF=\sqrt{(-4 - 1)^2+(1+1)^2}=\sqrt{(-5)^2+2^2}=\sqrt{25 + 4}=\sqrt{29}$.

Step3: Calculate length of FG

For points $F(-4,1)$ and $G(-3,4)$, $x_1=-4,y_1 = 1,x_2=-3,y_2 = 4$. Then $FG=\sqrt{(-3 + 4)^2+(4 - 1)^2}=\sqrt{1^2+3^2}=\sqrt{1 + 9}=\sqrt{10}$.

Step4: Use rectangle property

In a rectangle, opposite - sides are equal. So the perimeter $P=2(EF + FG)=2\sqrt{29}+2\sqrt{10}$.

Answer:

$2\sqrt{10}+2\sqrt{29}$ units