Question

what is the area of the rectangle below?

(-3,1), (1,-1), (7,2),(3,4)

Answer 1

To find the area of the rectangle, we need to find the distance between two opposite corners and multiply them.

Let's calculate the distance between (-3,1) and (1,-1) first:
Distance = sqrt((1 - (-3))^2 + (-1 - 1)^2) = sqrt((4)^2 + (-2)^2) = sqrt(16 + 4) = sqrt(20) = 2 * sqrt(5)

Now, let's calculate the distance between (1,-1) and (7,2):
Distance = sqrt((7 - 1)^2 + (2 - (-1))^2) = sqrt((6)^2 + (3)^2) = sqrt(36 + 9) = sqrt(45) = 3 * sqrt(5)

The area of the rectangle is:
Area = Distance1 * Distance2 = (2 * sqrt(5)) * (3 * sqrt(5)) = 6 * 5 = 30

Therefore, the area of the rectangle is 30.