Question

suppose a parallelogram is drawn on a coordinate plane. using verticies with coordinates (2,1), (2,3), (4,4), and (4,2), compute the perimeter. round your answer to the nearest tenth. (1 point) the perimeter is approximately 8.5 units. 8.0 9.5 8.2 8.5

Explanation:

Step1: Calculate the length of one pair of adjacent sides

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For the points \((2,1)\) and \((2,3)\):
\(d_1=\sqrt{(2 - 2)^2+(3 - 1)^2}=\sqrt{0 + 4}=2\)
For the points \((2,3)\) and \((4,4)\):
\(d_2=\sqrt{(4 - 2)^2+(4 - 3)^2}=\sqrt{4 + 1}=\sqrt{5}\approx2.2\)

Step2: Calculate the perimeter of the parallelogram

The perimeter \(P = 2(d_1 + d_2)\)
\(P=2(2 + 2.2)=2\times4.2 = 8.4\approx8.5\)

Answer:

\(8.5\)