Question

what is the perimeter of square abcd? d(-3, 5) a(3, 4) c(-4, -1) b(2, -2) √37 units 37 units 4√37 units 28 units

Explanation:

Step1: Use distance formula for side length

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For side $AB$ with $A(3,4)$ and $B(2,-2)$, we have $x_1 = 3,y_1 = 4,x_2=2,y_2=-2$. Then $d_{AB}=\sqrt{(2 - 3)^2+(-2 - 4)^2}=\sqrt{(-1)^2+(-6)^2}=\sqrt{1 + 36}=\sqrt{37}$.

Step2: Calculate perimeter of square

Since a square has all - sides equal, and perimeter $P$ of a square is $P = 4s$ (where $s$ is the side - length). Here $s=\sqrt{37}$, so $P = 4\sqrt{37}$.

Answer:

$4\sqrt{37}$ units