Question

1. what is the perimeter of the quadrilateral that is graphed below?

round your answer to the nearest whole number.

Explanation:

Step1: Label the vertices

Let the vertices of the quadrilateral be \(A(-2,3)\), \(B(0,1)\), \(C(2,1)\), \(D(4,3)\)

Step2: Calculate the length of \(AB\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
For \(A(-2,3)\) and \(B(0,1)\):
\(AB=\sqrt{(0 - (-2))^2+(1 - 3)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83\)

Step3: Calculate the length of \(BC\)

For \(B(0,1)\) and \(C(2,1)\):
\(BC=\sqrt{(2 - 0)^2+(1 - 1)^2}=\sqrt{4+0}=2\)

Step4: Calculate the length of \(CD\)

For \(C(2,1)\) and \(D(4,3)\):
\(CD=\sqrt{(4 - 2)^2+(3 - 1)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83\)

Step5: Calculate the length of \(DA\)

For \(D(4,3)\) and \(A(-2,3)\):
\(DA=\sqrt{(-2 - 4)^2+(3 - 3)^2}=\sqrt{36+0}=6\)

Step6: Calculate the perimeter

\(P = AB+BC + CD+DA\)
\(P\approx2.83+2+2.83+6\)
\(P\approx13.66\)

Answer:

\(14\)