Question

1. figure efgh in the coordinate plane has vertices at (-5,2), (-5,-2), (-1,-2), and (-1,2).

Explanation:

Step1: Determine the length of the horizontal side

For a horizontal side (e.g., \(EH\) or \(FG\)), use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) on a horizontal line (\(y_1 = y_2\)): \(d=\vert x_2 - x_1\vert\).
Take \(E(-5,2)\) and \(H(-1,2)\), then \(d=\vert-1-(-5)\vert=\vert-1 + 5\vert = 4\).

Step2: Determine the length of the vertical side

For a vertical side (e.g., \(EF\) or \(HG\)), use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) on a vertical line (\(x_1=x_2\)): \(d = \vert y_2 - y_1\vert\).
Take \(E(-5,2)\) and \(F(-5,-2)\), then \(d=\vert-2 - 2\vert=\vert-4\vert=4\).

Step3: Calculate the area of the square

Since all sides are equal (\(s = 4\)), and the area of a square \(A=s^2\).
So \(A = 4\times4=16\).

Answer:

\(16\)