Problem

Given three points A(1, 3), B(1, 1), and C(4, 1) on a plane, which are the vertices of a rectangle, find the perimeter of the rectangle.

Answer

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Answer

Substitute AB and BC into the formula: P=2(2+3)=10

Steps

Step 1 ：First, we need to calculate the side lengths AB and BC using the distance formula in analytic geometry. The distance formula is D=(x2−x1)2+(y2−y1)2

Step 2 ：Calculate AB: AB=(1−1)2+(1−3)2=22=2

Step 3 ：Calculate BC: BC=(4−1)2+(1−1)2=32=3

Step 4 ：The perimeter of a rectangle is given by the formula P=2(length+width)

Step 5 ：Substitute AB and BC into the formula: P=2(2+3)=10

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