What is the area of a rectangle with vertices at (1, 7) , (5, 3) , (3, 1) , and (−1, 5) ?Enter your answer in the box. units²

Answer:Area =  16 units²Step-by-step explanation:Points to rememberDistance formulaThe distance between two points (x1, y1) and (x2, y2) is given byDistance = √[(x2 - x1)² + (y2 - y1)²]To find the length and breadth of rectangleLet the points be  (1, 7) , (5, 3)Distance = √[(x2 - x1)² + (y2 - y1)²]  = √[(5 - 1)² + (3 - 7)²]  =  √[(4)² + (-4)²]  = √32 = 4√2If the points be  (5, 3) , (3, 1)Distance = √[(x2 - x1)² + (y2 - y1)²]  = √[(3 - 5)² + (1 - 3)²]  =  √[(-2)² + (-2)²]  = √8 = 2√2Length = 4√2 and breadth = 2√2To find the area of rectangleArea = Length * Breadth  = 4√2 * 2√2  = 16 units²