Question

Determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral triangle. Check all that apply.ScalenetriangleIsoscelestriangleEquilateraltriangle(a) T (2,0), R(-1, -2), 1 (2,6)(b) P(3,1), Q(-3, 1), R (0, 6)(C)D(-8,3), E(-1,0), F(-1, 6)O0OХ$?Continue

Answer 1

To solve this exercise, you have to determine the length of each side of the given triangles, compare the said lengths and classify the triangle.

Considering that you know the coordinates of each vertex of the triangles, the side lengths will be equal to the distance between each endpoint (vertex). To determine the distance between two points on the coordinate system you have to use the following formula:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Where

(x₁,y₁) are the coordinates of one of the points

(x₂,y₂) are the coordinates of one of the points

Triangle ΔTRI

Side TR

Endpoints T(2,0) and R(-1,-2)

Use the coordinates of T for (x₂,y₂) and the coordinates of R for (x₁,y₁)

`\begin{gathered} TR=\sqrt[]{(2-(-1))^2+(0-(-2))^2} \\ TR=\sqrt[]{(2+1)^2+(0+2)^2} \\ TR=\sqrt[]{3^2+2^2} \\ TR=\sqrt[]{9+4} \\ TR=\sqrt[]{13} \end{gathered}`

Side RI

Endpoints R(-1,-2) and I(2,6)

Use the coordinates of I for (x₂,y₂) and the coordinates of R for (x₁,y₁)

`\begin{gathered} RI=\sqrt[]{(2-(-1))^2+(6-(-2))^2} \\ RI=\sqrt[]{(2+1)^2+(6+2)^2} \\ RI=\sqrt[]{3^2+8^2} \\ RI=\sqrt[]{9+64} \\ RI=\sqrt[]{73} \end{gathered}`

Side IT

Endpoints I(2,6) and T(2,0)

Use the coordinates of I for (x₂,y₂) and the coordinates of T for (x₁,y₁)

`\begin{gathered} IT=\sqrt[]{(2-2)^2+(6-2)^2} \\ IT=\sqrt[]{0^2+4^2} \\ IT=\sqrt[]{16} \\ IT=4 \end{gathered}`

The side lengths of the triangle TRI are all different, which means that the triangle is a scalene triangle.