Question

find the perimeter of the parallelogram with these vertices.
(-2, 2), (-2, -2), (6, -1), (6, -5)
give an exact answer (not a decimal approximation).
simplify your answer as much as possible.

Explanation:

Step1: Find length of vertical side

The distance between \((-2, 2)\) and \((-2, -2)\) is \(|2 - (-2)| = 4\).

Step2: Find length of slant side

Using distance formula between \((-2, -2)\) and \((6, -1)\): \(\sqrt{(6 - (-2))^2 + (-1 - (-2))^2} = \sqrt{8^2 + 1^2} = \sqrt{65}\).

Step3: Calculate perimeter

Perimeter of parallelogram is \(2\times(4 + \sqrt{65}) = 8 + 2\sqrt{65}\).

Answer:

\(8 + 2\sqrt{65}\)