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Question: If the points (1,1), (–1, –1) and \(( - \sqrt{3},k)\) are vertices of an equilateral triangle then t...

If the points (1,1), (–1, –1) and (−3,k)( - \sqrt{3},k) are vertices of an equilateral triangle then the value of k will be.

A

1

B

–1

C

3\sqrt{3}

D

−3- \sqrt{3}

Answer

3\sqrt{3}

Explanation

Solution

l2=22+22=8=(3+1)2+(k−1)2⇒k=3l ^ { 2 } = 2 ^ { 2 } + 2 ^ { 2 } = 8 = ( \sqrt { 3 } + 1 ) ^ { 2 } + ( k - 1 ) ^ { 2 } \Rightarrow k = \sqrt { 3 }.