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

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Find distance $XY$

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

Step3: Find distance $YZ$

For points $Y(3,0)$ and $Z(-1,-2)$, $d_{YZ}=\sqrt{(-1 - 3)^2+(-2 - 0)^2}=\sqrt{(-4)^2+( - 2)^2}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}\approx4.47$.

Step4: Find distance $ZX$

For points $Z(-1,-2)$ and $X(-1,3)$, $d_{ZX}=\sqrt{(-1-(-1))^2+(3 - (-2))^2}=\sqrt{0^2+5^2}=5$.

Step5: Calculate perimeter

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

Answer:

$14.47$