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

Step 2 :Step 2: Calculate the length of AB using the coordinates of A(1,3) and B(4,3): \(AB = \sqrt{(4-1)^2 + (3-3)^2} = 3\)

Step 3 :Step 3: Calculate the length of BC using the coordinates of B(4,3) and C(4,1): \(BC = \sqrt{(4-4)^2 + (1-3)^2} = 2\)

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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