Question

A rectangle has the vertices below, find the area of the rectangle.

(9, −1), (−1, 7), (−5, 2), (5, −6)
(1 point)
Responses

41 square units
41 square units

82 square units
82 square units

123 square units
123 square units

205 square units

Answer 1

To find the area of a rectangle, we need to find the length of one side and the width of the rectangle.

Using the given coordinates:
The length of the rectangle can be calculated as the distance between points (9, -1) and (5, -6):

Length = sqrt((5-9)^2 + (-6-(-1))^2) = sqrt(16 + 25) = sqrt(41)

The width of the rectangle can be calculated as the distance between points (-1, 7) and (-5, 2):

Width = sqrt((-5-(-1))^2 + (2-7)^2) = sqrt(16 + 25) = sqrt(41)

Now, the area of the rectangle can be found by multiplying the length and width:

Area = Length * Width = sqrt(41) * sqrt(41) = 41 square units

So, the correct answer is:

41 square units.