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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]

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]

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Piyush
 
All the distances should be equal.
Hence
after removing square root sign,
a² + b² = 2² + (2\large \sqrt3)²
a² + b² = 16
 
Also
(a-2)² + (b- 2\large \sqrt3)² = 16
a² +4 -4a + b² + 12 - 4\large \sqrt3 b = 16
Now since a² + b² = 16
16 -4a -4\large \sqrt3 b +16 = 16
Hence
a + \large \sqrt3 b = 4
a = 4 - \large \sqrt3 b
Put thia in any equation and you will get a and then b.
 
Regards
Arun (askIITians forum expert)

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