Question

coordinate geometry distance in the coordinate plane
image long description
using the coordinates, what is the perimeter of the polygon? round each calculation to the nearest tenth

Explanation:

Step1: Find coordinates of points

From the graph, \(A(-1,-2)\), \(B(-2,0)\), \(C(0,2)\), \(D(2,0)\), \(E(1,-2)\)

Step2: Calculate length of \(AB\)

Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
For \(A(-1,-2)\) and \(B(-2,0)\)
\(AB=\sqrt{(-2 + 1)^2+(0 + 2)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.2\)

Step3: Calculate length of \(BC\)

For \(B(-2,0)\) and \(C(0,2)\)
\(BC=\sqrt{(0 + 2)^2+(2 - 0)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.8\)

Step4: Calculate length of \(CD\)

For \(C(0,2)\) and \(D(2,0)\)
\(CD=\sqrt{(2 - 0)^2+(0 - 2)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.8\)

Step5: Calculate length of \(DE\)

For \(D(2,0)\) and \(E(1,-2)\)
\(DE=\sqrt{(1 - 2)^2+(-2 - 0)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.2\)

Step6: Calculate length of \(EA\)

For \(E(1,-2)\) and \(A(-1,-2)\)
\(EA=\sqrt{(-1 - 1)^2+(-2 + 2)^2}=\sqrt{4+0}=2\)

Step7: Calculate perimeter

Perimeter \(P = AB + BC+CD + DE+EA\)
\(P\approx2.2+2.8+2.8+2.2+2\)
\(P\approx12.0\)

Answer:

\(12.0\)