Question

what is the area of a rectangle with vertices $(-8,-2)$, $(-3,-2)$, $(-3,-6)$, and $(-8,-6)$? square units

Explanation:

Step1: Calculate the length of the rectangle

The length can be found by calculating the distance between two points with the same \(y\)-coordinate. Using 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 the points \((-8,-2)\) and \((-3,-2)\). Then \(l=\vert-3-(-8)\vert=\vert-3 + 8\vert = 5\).

Step2: Calculate the width of the rectangle

The width can be found by calculating the distance between two points with the same \(x\)-coordinate. Using 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 the points \((-3,-2)\) and \((-3,-6)\). Then \(w=\vert-6-(-2)\vert=\vert-6 + 2\vert=4\).

Step3: Calculate the area of the rectangle

The area formula for a rectangle is \(A=l\times w\).
Substitute \(l = 5\) and \(w = 4\) into the formula: \(A=5\times4=20\).

Answer:

\(20\)