Find the lengths of the sides of the triangle by using the Distance Formula.
Is â–ł ABC an Equilateral Triangle? No. Explanation: See solution.
Practice makes perfect
To begin, let's plot the given points on a coordinate plane and graph the triangle.
Now we will determine whether it is an equilateral triangle.
Classifying the Triangle
Let's begin by reviewing the definitions of a scalene, isosceles, and equilateral triangles.
Scalene: a triangle with three sides all of different lengths.
Isosceles: a triangle with two sides of equal length.
Equilateral: a triangle with all sides of equal length.
To classify our triangle we will find the length of each side using the Distance Formula.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Simplify
AB
A( 2,3), B( 10,9)
sqrt(( 10- 2)^2+( 9- 3)^2)
10
BC
B( 10,9), C( 10, -3)
sqrt(( 10- 10)^2+( -3- 9)^2)
12
CA
C( 10, -3), A( 2,3)
sqrt(( 2-( 10))^2+( 3-( -3))^2)
10
As we can see, one side of our triangle has a different length. Therefore, it is an isosceles triangle. Because of that, the triangle is not an equilateral triangle.
