Question

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

Explanation:

Step1: Find coordinates of points

Assume \(X(2,2)\), \(Y(4,-2)\), \(Z(-3,-4)\) (coordinates from graph).

Step2: Calculate distance \(XY\)

Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(XY\): \(x_1 = 2,y_1 = 2,x_2 = 4,y_2=-2\)
\(XY=\sqrt{(4 - 2)^2+(-2 - 2)^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.47\)

Step3: Calculate distance \(YZ\)

For \(YZ\): \(x_1 = 4,y_1=-2,x_2=-3,y_2=-4\)
\(YZ=\sqrt{(-3 - 4)^2+(-4 + 2)^2}=\sqrt{49 + 4}=\sqrt{53}\approx7.28\)

Step4: Calculate distance \(ZX\)

For \(ZX\): \(x_1=-3,y_1=-4,x_2 = 2,y_2 = 2\)
\(ZX=\sqrt{(2 + 3)^2+(2 + 4)^2}=\sqrt{25+36}=\sqrt{61}\approx7.81\)

Step5: Calculate perimeter

Perimeter \(P=XY + YZ+ZX\approx4.47+7.28 + 7.81=19.56\approx19.6\)

Answer:

\(19.6\)