Question

graph the following figure in the coordinate plane. find the perimeter. x(0,1), y(4, - 2), z(-5, - 2)

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: Calculate distance $XY$

For points $X(0,1)$ and $Y(4,-2)$, we have $x_1 = 0,y_1 = 1,x_2 = 4,y_2=-2$.
$XY=\sqrt{(4 - 0)^2+(-2 - 1)^2}=\sqrt{4^2+(-3)^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step3: Calculate distance $YZ$

For points $Y(4,-2)$ and $Z(-5,-2)$, we have $x_1 = 4,y_1=-2,x_2=-5,y_2 = -2$.
$YZ=\sqrt{(-5 - 4)^2+(-2+2)^2}=\sqrt{(-9)^2+0^2}=\sqrt{81}=9$.

Step4: Calculate distance $ZX$

For points $Z(-5,-2)$ and $X(0,1)$, we have $x_1=-5,y_1=-2,x_2 = 0,y_2 = 1$.
$ZX=\sqrt{(0 + 5)^2+(1 + 2)^2}=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}$.

Step5: Calculate perimeter

The perimeter $P=XY + YZ+ZX=5 + 9+\sqrt{34}=14+\sqrt{34}$.

Answer:

$14+\sqrt{34}$