Let's plot the points A, B, and C, and draw â–³ ABC.
We are asked to prove whether this triangle is equilateral. To do this, we will verify if all three sides are congruent. We can do this by determining the length of each side using the Distance Formula.
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
Let's substitute the values to find each side length!
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
Side Length
Points
Substitute
Simplify
AB
A( 0,0) and B( 6,0)
AB=sqrt(( 6- 0)^2 + ( 0 - 0)^2)
AB=6
AC
A( 0,0) and C( 3,3sqrt(3))
AC=sqrt(( 3- 0)^2+( 3sqrt(3)- 0)^2)
AC=6
BC
B( 6,0) and C( 3,3sqrt(3))
BC=sqrt(( 3 - 6)^2+( 3sqrt(3)- 0)^2)
BC=6
Because all side lengths are equal, all three sides are congruent. Therefore, â–³ ABC is an equilateral triangle.
