Question

show that the points (1,1),(-1,-1),(-√3,√3)form an equilateral traingle​

Answer 1

Step-by-step explanation:

Let the points are A(1,1),B(-1,-1),C(-√3,√3)

Now distance between A and B

_________

=AB=√(1+1)²+(1+1)²

_____

= √2²+2²

____

=√4+4. =√8=2√2

Distance between B and C

_____________

= BC=√(-1+√3)²+(-1-√3)²

___________

=√(√3-1)²+(√3+1)²

________

=√2×{(√3)²+1²}

=√2×4=√8=2√2

Distance between A and C

=√(1+√3)²+(1-√3)²=2√2. (as above l

As AB=BC=AC, so triangle ABC is an equilateral triangle.

hope you got it