Problem

Given four points A(1,3), B(4,3), C(4,1) and D(1,1) in a two-dimensional plane, what is the perimeter of the rectangle formed by these points?

Answer

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Answer

Step 5: Substitute the lengths calculated in steps 2 and 3 into the formula in step 4: P=2∗(3+2)

Steps

Step 1 ：Step 1: Use the formula of distance between two points in the plane to calculate the lengths of the sides of the rectangle. The formula is d=(x2−x1)2+(y2−y1)2

Step 2 ：Step 2: Calculate the length of AB using the coordinates of A(1,3) and B(4,3): AB=(4−1)2+(3−3)2=3

Step 3 ：Step 3: Calculate the length of BC using the coordinates of B(4,3) and C(4,1): BC=(4−4)2+(1−3)2=2

Step 4 ：Step 4: The perimeter of a rectangle is twice the sum of the length and width: P=2∗(length+width)

Step 5 ：Step 5: Substitute the lengths calculated in steps 2 and 3 into the formula in step 4: P=2∗(3+2)

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