Question

show that the point (a,a),(-a,-a),(-√3a,√3a) are the vertices of the equilateral triangle. also find its area

Answer 1

hope it will help you

Answer 2

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