What is the area of the rectangle below?
(-3,1). (3,4). (7,2). (1,1)
2√5
3√5
10√5
30
Please help
To find the area of the rectangle formed by the four points (-3,1), (3,4), (7,2), and (1,1), we need to find the length of two adjacent sides of the rectangle and then multiply them together.
Using the distance formula, the length of the side between (-3,1) and (3,4) is:
√((3-(-3))^2 + (4-1)^2) = √((6)^2 + (3)^2) = √(36 + 9) = √45 = 3√5
Similarly, the length of the side between (7,2) and (3,4) is:
√((7-3)^2 + (2-4)^2) = √((4)^2 + (-2)^2) = √(16 + 4) = √20 = 2√5
Therefore, the area of the rectangle is the product of the two adjacent side lengths:
3√5 * 2√5 = 6√25 = 6 * 5 = 30
So, the area of the rectangle is 30.