Question

graph the following figure in the coordinate - plane. find the perimeter. x(0,1), y(4, - 2), z( - 5, - 2). choose the correct graph below. the perimeter of △xyz is units. (simplify your answer. round to one decimal place as needed.)

Explanation:

Step1: Recall 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 $x_1 = 0,y_1=1,x_2 = 4,y_2=-2$. Then $XY=\sqrt{(4 - 0)^2+(-2 - 1)^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step3: Calculate distance $YZ$

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

Step4: Calculate distance $ZX$

For points $Z(-5,-2)$ and $X(0,1)$, we have $x_1=-5,y_1=-2,x_2 = 0,y_2=1$. Then $ZX=\sqrt{(0 + 5)^2+(1 + 2)^2}=\sqrt{25+9}=\sqrt{34}\approx5.8$.

Step5: Calculate perimeter

The perimeter $P$ of $\triangle XYZ$ is $P=XY + YZ+ZX=5 + 9+5.8 = 19.8$.

Answer:

$19.8$