What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ? enter your answer in the box. do not round any side lengths. units²

16 First, determine the lengths of each side by using the Pythagorean theorem. Distance between (-3,-1) and (1,3) sqrt((-3 - 1)^2 + (-1 -3)^2) = sqrt(-4^2 + -4^2) = sqrt(16 + 16) = sqrt(32) = 4sqrt(2) Do the same thing to determine the distances between the other vertexes Distance (1,3) to (3,1) = 2sqrt(2) Distance (3,1) to (-1,-3) = 4sqrt(2) Distance (-1,-3) to (-3,-1) = 2sqrt(2) We now know that the rectangle has a length of 4sqrt(2) and a height of 2sqrt(2). Since the area is simply the product of those two values, we get: 4sqrt(2) * 2sqrt(2) = 4 * 2 * sqrt(2)*sqrt(2) = 4 * 2 * 2 = 16.