Question

δxyz is shown on the graph below. each unit on the graph measures 1 centimeter. the perimeter of δxyz is approximately cm.

Explanation:

Step1: Find coordinates of points

Let \(X(3,2)\), \(Y(5, - 2)\), \(Z(-3,-4)\)

Step2: Use distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(XY\):
\(x_1 = 3,y_1 = 2,x_2 = 5,y_2=-2\)
\(XY=\sqrt{(5 - 3)^2+(-2 - 2)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47\)
For \(YZ\):
\(x_1 = 5,y_1=-2,x_2=-3,y_2=-4\)
\(YZ=\sqrt{(-3 - 5)^2+(-4 + 2)^2}=\sqrt{64 + 4}=\sqrt{68}=2\sqrt{17}\approx8.25\)
For \(ZX\):
\(x_1=-3,y_1=-4,x_2 = 3,y_2 = 2\)
\(ZX=\sqrt{(3 + 3)^2+(2 + 4)^2}=\sqrt{36+36}=\sqrt{72}=6\sqrt{2}\approx8.49\)

Step3: Calculate perimeter \(P=XY + YZ+ZX\)

\(P\approx4.47+8.25 + 8.49=21.21\)

Answer:

\(21.21\)