Problem

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?

Answer

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Answer

Since the area of a rectangle is given by the product of the lengths of its sides, the area of ABCD is 3×4=12.

Steps

Step 1 ：First, calculate the length of the sides of the rectangle using the distance formula. The distance between two points (x1,y1) and (x2,y2) is given by (x2−x1)2+(y2−y1)2.

Step 2 ：The length of AB is (5−2)2+(2−2)2=3.

Step 3 ：The length of BC is (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 3×4=12.

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