What is the area of the rectangle? (-3,1), (3,4), (1,1), (7,2) a. 2√5 b. 3√5 c. 10√5 d. 30
To find the area of the rectangle, we need to find the length of the sides.
The lengths of the sides can be found using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points:
Side 1: (-3,1) and (3,4)
d = √((3 - (-3))^2 + (4 - 1)^2) = √(6^2 + 3^2) = √(36 + 9) = √45 = 3√5
Side 2: (3,4) and (1,1)
d = √((1 - 3)^2 + (1 - 4)^2) = √((-2)^2 + (-3)^2) = √(4 + 9) = √13
The area of a rectangle is calculated by multiplying the length of the sides:
Area = Side 1 * Side 2 = 3√5 * √13 = 3√65
Therefore, the area of the rectangle is not one of the given answer choices.