Question

suppose a parallelogram is drawn on a coordinate plane. using vertices 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 units. 8.0 8.5 9.5 8.2

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 \(P = 2(d_1 + d_2)\)
\(P=2(2 + 2.2)=2\times4.2 = 8.4\approx8.5\) (after re - checking with more accurate calculation of \(\sqrt{5}\approx2.236\), \(P = 2(2+\sqrt{5})=4 + 2\sqrt{5}\approx4+4.472 = 8.472\approx8.5\))

Answer:

\(8.5\)