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. scratch area (not part of answer) perimeter:

Explanation:

Step1: Calculate the length of one pair of parallel sides

For the points \((-2,2)\) and \((-2, - 2)\), since the \(x\) - coordinates are the same (\(x=-2\)), we use the distance formula for vertical distance \(d=\vert y_2 - y_1\vert\).
Let \(y_1 = 2\) and \(y_2=-2\), then \(d_1=\vert-2 - 2\vert=\vert-4\vert = 4\).

Step2: Calculate the length of the other pair of parallel sides

For the points \((-2,-2)\) and \((3,-2)\), since the \(y\) - coordinates are the same (\(y = - 2\)), we use the distance formula for horizontal distance \(d=\vert x_2 - x_1\vert\).
Let \(x_1=-2\) and \(x_2 = 3\), then \(d_2=\vert3-(-2)\vert=\vert3 + 2\vert=5\).

Step3: Use the perimeter formula for a parallelogram

The perimeter formula of a parallelogram is \(P = 2(a + b)\), where \(a\) and \(b\) are the lengths of adjacent sides.
Here \(a = 4\) and \(b = 5\), so \(P=2(4 + 5)\).

Answer:

\(18\)