Question

find the perimeter of the polygon with the vertices x(-1, 3), y(3, 0), and z(-1, -2). round your answer to the nearest hundredth. the perimeter is about units

Explanation:

Step1: Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

For side $XY$ with $X(-1,3)$ and $Y(3,0)$:
$d_{XY}=\sqrt{(3 - (-1))^2+(0 - 3)^2}=\sqrt{(4)^2+(-3)^2}=\sqrt{16 + 9}=\sqrt{25}=5$

Step2: For side $YZ$ with $Y(3,0)$ and $Z(-1,-2)$

$d_{YZ}=\sqrt{(-1 - 3)^2+(-2 - 0)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}\approx 4.47$

Step3: For side $ZX$ with $Z(-1,-2)$ and $X(-1,3)$

$d_{ZX}=\sqrt{(-1-(-1))^2+(3 - (-2))^2}=\sqrt{(0)^2+(5)^2}=5$

Step4: Calculate perimeter $P$

$P=d_{XY}+d_{YZ}+d_{ZX}=5 + 2\sqrt{5}+5=10 + 2\sqrt{5}\approx10+4.47 = 14.47$

Answer:

$14.47$