Question

the coordinates of three vertices of square abcd are (a(-2\frac{1}{2},1\frac{1}{2})), (b(-2\frac{1}{2}, - 3)), and (c(2,1\frac{1}{2})). when point d is placed on this square, what will the perimeter of the square be? enter your answer in the box.

Explanation:

Step1: Find side - length using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let's find the distance between $A(-2\frac{1}{2},1\frac{1}{2})$ and $B(-2\frac{1}{2}, - 3)$. Here $x_1=-2.5,y_1 = 1.5,x_2=-2.5,y_2=-3$. Then $d=\sqrt{(-2.5+2.5)^2+(-3 - 1.5)^2}=\sqrt{0+( - 4.5)^2}=4.5$.

Step2: Calculate the perimeter of the square

The perimeter $P$ of a square with side - length $s$ is $P = 4s$. Since $s = 4.5$, then $P=4\times4.5 = 18$.

Answer:

18