Question

Find the perimeter of the triangle defined by the coordinates (9, 0), (-5, 0), and (-10, 6). (Round to nearest tenth)

Answer 1

The perimeter is 41.7.

We first find the distance between each vertex using the distance formula:
$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\=\sqrt{(0-0)^2+(-5-9)^2}=\sqrt{0^2+(-14)^2}=\sqrt{196}=14 \\ \\d=\sqrt{(6-0)^2+(-10--5)^2}=\sqrt{6^2+(-5)^2}=\sqrt{36+25}=\sqrt{61} \\=7.81 \\ \\d=\sqrt{(6-0)^2+(-10-9)^2}=\sqrt{6^2+(-19)^2}=\sqrt{36+361}=\sqrt{397} \\=19.92$

We now find the perimeter by adding all of the side lengths:
14+7.81+19.92 = 41.73 ≈ 41.7