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Question

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=(2a2a)2+(6a4a)2=4a2=2|a|
BC=(2a+3a2a)2+(5a6a)2=4a2=2|a|
and AC=(2a+3a2a)2+(5a4a)2=4a2=2|a|
Since, AB=BC=CA, hence points A,B and C are the vertices of an equilateral triangle.

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