Question

click on the graph to plot a point. click a point to delete it. answer attempt 1 out of 3 perimeter = units submit answer

Explanation:

Step1: Identify the coordinates of vertices

Assume the vertices of the polygon are \(D(0,0)\), let's say \(B(x_1,y_1)\) and \(C(x_2,y_2)\). From the graph, if we assume \(B(6, - 9)\) and \(C(7,-2)\).

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

For side \(DB\): \(d_{DB}=\sqrt{(6 - 0)^2+(-9 - 0)^2}=\sqrt{36 + 81}=\sqrt{117}=3\sqrt{13}\)
For side \(BC\): \(d_{BC}=\sqrt{(7 - 6)^2+(-2+9)^2}=\sqrt{1 + 49}=\sqrt{50}=5\sqrt{2}\)
For side \(CD\): \(d_{CD}=\sqrt{(0 - 7)^2+(0 + 2)^2}=\sqrt{49+4}=\sqrt{53}\)

Step3: Calculate the perimeter \(P\)

\(P=d_{DB}+d_{BC}+d_{CD}\)
\(P = 3\sqrt{13}+5\sqrt{2}+\sqrt{53}\approx3\times3.606+5\times1.414 + 7.280\)
\(P\approx10.818+7.07+7.280=25.168\approx25.17\)

Answer:

\(3\sqrt{13}+5\sqrt{2}+\sqrt{53}\) (or approximately \(25.17\))