Given four points in the Cartesian plane, A(2,2), B(5,2), C(5,6), and D(2,6), what is the area of the rectangle formed by these points?

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Accepted Answer

Step:1 ：First, calculate the length of the sides of the rectangle using the distance formula. The distance between two points ((x_1, y_1)) and ((x_2, y_2)) is given by (sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}).Step:2 ：The length of AB is (sqrt{(5 - 2)^2 + (2 - 2)^2} = 3).Step:3 ：The length of BC is (sqrt{(5 - 5)^2 + (6 - 2)^2} = 4).Step:4 ：Since the area of a rectangle is given by the product of the lengths of its sides, the area of ABCD is (3 times 4 = 12).

Answer

Step: 1 ：First, calculate the length of the sides of the rectangle using the distance formula. The distance between two points ((x_1, y_1)) and ((x_2, y_2)) is given by (sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}).Step: 2 ：The length of AB is (sqrt{(5 - 2)^2 + (2 - 2)^2} = 3).Step: 3 ：The length of BC is (sqrt{(5 - 5)^2 + (6 - 2)^2} = 4).Step: 4 ：Since the area of a rectangle is given by the product of the lengths of its sides, the area of ABCD is (3 times 4 = 12).

Given four points in the Cartesian plane, A(2,2), B(5,2), C(5,6), and D(2,6), what is the area of the rectangle formed by these points?

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