Question

find the perimeter and area of the rectangle with vertices (5, -7), (5, 1), (-2, 1), and (-2, -7). note that you can draw in the scratch area below, but it is not part of the answer. scratch area (not part of answer) perimeter: units area: square units

Explanation:

Step1: Find the length and width

For vertical side (same \(x\) - coordinate):
Use the distance formula for two points \((x_1,y_1)\) and \((x_1,y_2)\) which is \(d=\vert y_2 - y_1\vert\).
Take \((5,1)\) and \((5, - 7)\), then \(l=\vert1-(-7)\vert=\vert1 + 7\vert = 8\)
For horizontal side (same \(y\) - coordinate):
Use the distance formula for two points \((x_1,y_1)\) and \((x_2,y_1)\) which is \(d=\vert x_2 - x_1\vert\).
Take \((5,1)\) and \((-2,1)\), then \(w=\vert5-(-2)\vert=\vert5 + 2\vert=7\)

Step2: Calculate the perimeter

The formula for the perimeter of a rectangle is \(P = 2(l + w)\)
Substitute \(l = 8\) and \(w = 7\) into the formula:
\(P=2(8 + 7)=2\times15 = 30\)

Step3: Calculate the area

The formula for the area of a rectangle is \(A=l\times w\)
Substitute \(l = 8\) and \(w = 7\) into the formula:
\(A=8\times7=56\)

Answer:

Perimeter: \(30\) units
Area: \(56\) square units