Question

graph the following figure in the coordinate plane. find the perimeter.
x(0,1), y(3, -3), z(-7, -3)

choose the correct graph below.
a. graph, b. graph, c. graph

the perimeter of δxyz is \\(\square\\) units.
(simplify your answer. round to one decimal place as needed.)

Explanation:

Step1: Find length of YZ

Points Y(3, -3) and Z(-7, -3) have same y - coordinate. So length \( YZ=\vert3 - (-7)\vert = 10\).

Step2: Find length of XY

Using distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \) for X(0,1) and Y(3, -3):
\( XY=\sqrt{(3 - 0)^2+(-3 - 1)^2}=\sqrt{9 + 16}=\sqrt{25}=5 \)

Step3: Find length of XZ

Using distance formula for X(0,1) and Z(-7, -3):
\( XZ=\sqrt{(-7 - 0)^2+(-3 - 1)^2}=\sqrt{49 + 16}=\sqrt{65}\approx8.1 \)

Step4: Calculate perimeter

Perimeter \( = YZ+XY + XZ=10 + 5+\sqrt{65}\approx10 + 5+8.1 = 23.1 \)

Answer:

23.1