Question

name
homework
2 - 6
assigned 10/9
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?

Explanation:

Step1: Calculate the side length using the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For points \(A(-2\frac{1}{2},1\frac{1}{2})\) and \(B(-2\frac{1}{2},- 3)\), \(x_1=-2.5,y_1 = 1.5,x_2=-2.5,y_2=-3\).
\(d=\sqrt{(-2.5+2.5)^2+(-3 - 1.5)^2}=\sqrt{0+( - 4.5)^2}=4.5\)

Step2: Calculate the perimeter of the square

The perimeter formula of a square is \(P = 4s\), where \(s\) is the side - length of the square.
Since \(s = 4.5\), then \(P=4\times4.5 = 18\)

Answer:

\(18\)