The points (2a,4a),(2a,6a) and (2a+√3a,5a) are the vertices of
A
an isosceles triangle
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B
an equilateral triangle
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C
a right-angled isosceles triangle
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D
a scalene triangle
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Solution
The correct option is B an equilateral triangle Let A≡(2a,4a),B≡(2a,6a) and C≡(2a+√3a,5a)
Now, AB=√(2a−2a)2+(6a−4a)2=√4a2=2|a| BC=√(2a+√3a−2a)2+(5a−6a)2=√4a2=2|a|
and AC=√(2a+√3a−2a)2+(5a−4a)2=√4a2=2|a|
Since, AB=BC=CA, hence points A,B and C are the vertices of an equilateral triangle.