Question

the graph shows the endpoints of one side of a parallelogram. determine the perimeter of the parallelogram. enter the unknown segment length(s), then calculate the perimeter of the polygon. perimeter of the parallelogram: units a (-21, 3) b (-2, 17) e (-2, 3) d = \sqrt{( )^{2}+( )^{2}} d =

Explanation:

Step1: Find the length of side AB using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(-21,3)$ and $B(-2,17)$, we have $x_1=-21,y_1 = 3,x_2=-2,y_2 = 17$. Then $d_{AB}=\sqrt{(-2+21)^2+(17 - 3)^2}=\sqrt{(19)^2+(14)^2}=\sqrt{361+196}=\sqrt{557}$.

Step2: Recall property of parallelogram

In a parallelogram, opposite sides are equal. Let the given side be $AB$ and its opposite side be $CD$, and the other - pair of opposite sides be $AD$ and $BC$. The length of the vertical side (from the graph) is $17 - 3=14$ and the length of the horizontal - like side (from the graph) is $-2+21 = 19$.
The perimeter $P$ of a parallelogram with adjacent side lengths $a$ and $b$ is $P = 2(a + b)$. Here $a=\sqrt{557}$ and $b = 14$.
$P=2(\sqrt{557}+14)=2\sqrt{557}+28$.

Answer:

$2\sqrt{557}+28$