Analytical Geometry> If the points (0,0),(2,2√3),and (a, b) be...

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]

Piyush Upadhyay , 8 Years ago

Grade 11

1 Answers

Arun

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

Arun (askIITians forum expert)

Approved

Last Activity: 8 Years ago

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Analytical Geometry> If the points (0,0),(2,2√3),and (a, b) be...

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]

Piyush Upadhyay , 8 Years ago

Arun

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