Question

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.

Answer 1

Area (a) = length (l) × width (w), so we need the distance formula between 2 points for each one width and one length:

`d = \sqrt{{(y2 - y1)}^(2) + {(x2 - x1)}^(2) }`

`w = \sqrt{{(1 - 3)}^(2) + {(3 - 1)}^(2) } \\ = \sqrt{( {( - 2)}^(2) + {(2)}^(2))} = √(4 + 4) \\ = √(8) \: =`

`l = \sqrt{({(3 - - 1)}^(2) + {(1 - - 3)}^(2))} \\ = \sqrt{({(3 + 1)}^(2) + {(1 + 3)}^(2))} \\ = \sqrt{({(4)}^(2) + {(4)}^(2))} \\ = \sqrt{({16} + {16})} \: = √(32)`

`a \: = l * w = √(32) * √(8) \\ = √(256) = 16 \: {units}^(2)`