# If the points (0,0),(2,2√3),and (a, b) be the vertices of an equilateral triangle🔺 ,then (a, b) =1](0,-4)2](0,4)3](4,0)4](-4,0)Please explain how you solved it with correct answer. The correct answer is [3]

Arun
25757 Points
5 years ago
Dear Piyush

All the distances should be equal.
Hence
after removing square root sign,
a² + b² = 2² + (2$\large \sqrt$3)²
a² + b² = 16

Also
(a-2)² + (b- 2$\large \sqrt$3)² = 16
a² +4 -4a + b² + 12 - 4$\large \sqrt$3 b = 16
Now since a² + b² = 16
16 -4a -4$\large \sqrt$3 b +16 = 16
Hence
a + $\large \sqrt$3 b = 4
a = 4 - $\large \sqrt$3 b
Put thia in any equation and you will get a and then b.

Regards