Question

Show that the points (a,a) , (-a,-a) and (-√3, √3) are the vertices of an equilateral triangle.

Answer 1

A(a,a)

B(-a,-a)

C(-√3a,√3a)

AB=√(-a-a)²+(-a-a)²

=√(-2a)²+(-2a)²

=√4a² + 4a²

=√8a²

=2√2a

BC=√(-√3+a)² + (√3a+a)²

= √(1-√3)²+(√3+a)²

=a√1+3-2√3+3+1+2√3

a√8

2√2a

AC=√(-√3a-a)²+(√3a-a)²

=√(-√3-1)²a²+(√3a-a)²

=a√3+1+2√3+3+1-2√3

=a√8

=2√2a

therefore AC=BC=AC. It is a equilateral triangle

please mark as brainliest answer

Answer 2

Let A(a,a) ,B(-a,-a),C(-/3,/3)
Find Distance AB,BC,AC using distance formula if AB=BC=CA only then ABC is an equilateral triangle otherwise no