Question

a quadrilateral has vertices (3, 5), (6, 9), (10, 9), and (10, 5). what is the perimeter of the quadrilateral?

Explanation:

Step1: Calculate the length of the first side

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for the points \((3,5)\) and \((6,9)\).
\(d_1=\sqrt{(6 - 3)^2+(9 - 5)^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

Step2: Calculate the length of the second side

For the points \((6,9)\) and \((10,9)\), since \(y\) - coordinates are the same.
\(d_2=\vert10 - 6\vert=4\)

Step3: Calculate the length of the third side

For the points \((10,9)\) and \((10,5)\), since \(x\) - coordinates are the same.
\(d_3=\vert9 - 5\vert=4\)

Step4: Calculate the length of the fourth side

For the points \((10,5)\) and \((3,5)\), since \(y\) - coordinates are the same.
\(d_4=\vert10 - 3\vert=7\)

Step5: Calculate the perimeter

Perimeter \(P=d_1 + d_2 + d_3 + d_4\)
\(P=5+4 + 4+7=20\)

Answer:

\(20\)