Question

find the perimeter of the parallelogram with these vertices. (-2,2), (-2,-2), (3,-2), (3,-6) give an exact answer (not a decimal approximation). simplify your answer as much as possible.

Explanation:

Step1: Find the length of one pair of sides

Use the distance formula for vertical sides (same \(x -\)coordinate). For \((-2,2)\) and \((-2,-2)\):
\(d=\vert y_2 - y_1\vert=\vert-2 - 2\vert = 4\)

Step2: Find the length of the other pair of sides

Use the distance formula for horizontal sides (same \(y -\)coordinate). For \((-2,-2)\) and \((3,-2)\):
\(d=\vert x_2 - x_1\vert=\vert3-(-2)\vert = 5\)

Step3: Calculate the perimeter of the parallelogram

The perimeter \(P\) of a parallelogram is \(P = 2(a + b)\), where \(a = 4\) and \(b = 5\)
\(P=2(4 + 5)=2\times9\)

Answer:

\(18\)