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What is the perimeter of a rectangle with vertices at (3,2) (-2,2) (-2,-2) and (3,-2

User Pikalek
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1 Answer

3 votes

To find the perimeter

Let ABCD be the vertices of (3,2) (-2,2) (-2,-2) and (3,-2​) respectively

A(3,2) B (-2,2) C(-2,-2) and D (3,-2)

We will find the distance AB, BC, CD and DA

Using the distance formula;


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

Find the distance AB

A(3,2) B (-2,2)

x₁ = 3 y₁=2 x₂=-2 y₂=2

substituting the value into the formula:


|AB|=\sqrt[]{(-2-3)^2+(2-2)^2}

Evaluate


|AB|=\sqrt[]{(-5)^2+0}
=\sqrt[]{25}


=5

Find the distance BC

B (-2,2) C(-2,-2)

x₁ = -2 y₁=2 x₂=-2 y₂=-2

Substitute into the formula


|BC|=\sqrt[]{(-2+2)^2+(-2-2)^2}

Evaluate


=\sqrt[]{0+(-4)^2}


=\sqrt[]{16}
=4

Find the distance CD

C(-2,-2) D (3,-2)

x₁ = -2 y₁=-2 x₂=-3 y₂=-2

Substitute into the formula


|CD|=\sqrt[]{(-3+2)^2+(-2+2)^2}

Evaluate


|CD|=\sqrt[]{(-5)^2+0}
=\sqrt[]{25}
=5

Find the distance DA

D(3 -2) A(3, 2)

x₁ = 3 y₁=-2 x₂=3 y₂=2

Substitute into the formula


|DA|=\sqrt[]{(3-3)^2+(2+2)^2}

Evaluate


=\sqrt[]{0+4^2}
=\sqrt[]{16}
=4

To get the perimeter, we will add all the distance

That is:

Perimeter = AB + BC + CD + DA

=5 + 4 + 5 + 4

=18

Perimeter = 18

User Tida
by
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