Question

challenge: 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

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for points \(A(-2.5,1.5)\) and \(B(-2.5,-3)\).
\(x_1=-2.5,y_1 = 1.5,x_2=-2.5,y_2=-3\)
\(d=\sqrt{(-2.5+2.5)^2+(-3 - 1.5)^2}=\sqrt{0+(-4.5)^2}=4.5\)

Step2: Calculate the perimeter

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

Answer:

\(18\)