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Question
If three points (0, 0), \[\left( 3, \sqrt{3} \right)\] and (3, λ) form an equilateral triangle, then λ =
Options
2
-3
-4
None of these
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Solution
We have an equilateral triangle ΔABC whose co-ordinates are A (0, 0); B ` ( 3 ,sqrt(3))" and " C (3 , λ )` .
Since the triangle is equilateral. So,
`AB^2 = Ac^2`
So,
`(3 - 0)^2 + (sqrt(3) - 0)^2 = (3 - 0)^2 + (lambda - 0)^2`
Cancel out the common terms from both the sides,
Therefore,
`lambda = sqrt(3)`
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