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Question

Assertion :If A(2a, 4a) and B(2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a+a3,5a). Reason: In equilateral triangle all the coordinates of three vertices can be rational.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is C Assertion is correct but Reason is incorrect
Assertion:-
If A(2a,4a),B(2a,6a) and C(2a+a3,5a) are the vertics of an equilateral triangle,then
AB=(2a2b)2+(6a4a)2=2aBC=(2a+a32a)2+(5a6a)2=3a2+a2=2aAC=(2a+a32a)2+(5a4a)2=3a2+a2=2a
as AB=BC=CA
there are the vertics of an equilateral triangle
But the reason is wrong,explanation for assertion.Such that,an equilateral triangle all the coordinate of three verticall is wrong

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