Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. parallelogram rstu

Explanation:

Step1: Identify side - lengths using distance formula

For a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$, the distance $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. In a parallelogram, opposite sides are equal. Let's assume the coordinates of the vertices: $R(-18,15)$, $S(-6,15)$, $T(0,3)$, $U(-12,3)$.
The length of $RS$: Since $y$-coordinates are the same ($y = 15$ for both $R$ and $S$), $RS=\vert-6-(-18)\vert=\vert-6 + 18\vert=12$.
The length of $ST$: Using the distance formula with $S(-6,15)$ and $T(0,3)$, $d_{ST}=\sqrt{(0 + 6)^2+(3 - 15)^2}=\sqrt{6^2+(-12)^2}=\sqrt{36 + 144}=\sqrt{180}=6\sqrt{5}\approx13.42$.

Step2: Calculate the perimeter of the parallelogram

The perimeter $P$ of a parallelogram with adjacent - side lengths $a$ and $b$ is $P = 2(a + b)$. Here, $a = 12$ and $b\approx13.42$. So $P=2(12 + 13.42)=2\times25.42 = 50.84$.

Answer:

$50.84$