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 \(D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Step 2 ：Calculate AB: \(AB = \sqrt{(1 - 1)^2 + (1 - 3)^2} = \sqrt{2^2} = 2\)

Step 3 ：Calculate BC: \(BC = \sqrt{(4 - 1)^2 + (1 - 1)^2} = \sqrt{3^2} = 3\)

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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