We first find the distance between each vertex using the distance formula: [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}
\\
\\=\sqrt{(0-0)^2+(-5-9)^2}=\sqrt{0^2+(-14)^2}=\sqrt{196}=14
\\
\\d=\sqrt{(6-0)^2+(-10--5)^2}=\sqrt{6^2+(-5)^2}=\sqrt{36+25}=\sqrt{61}
\\=7.81
\\
\\d=\sqrt{(6-0)^2+(-10-9)^2}=\sqrt{6^2+(-19)^2}=\sqrt{36+361}=\sqrt{397}
\\=19.92[/tex]
We now find the perimeter by adding all of the side lengths: 14+7.81+19.92 = 41.73 ≈ 41.7
