Assertion -If A2a- 4a and B2a- 6a are two vertices of a equilateral triangle ABC then the vertex C is given by 2a-a-3- 5a- Reason- In equilateral triangle all the coordinates of three vertices can be rational-

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Collinear Vectors

Assertion :If...

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 $(2 a + a \sqrt{3}, 5 a) .$ Reason: In equilateral triangle all the coordinates of three vertices can be rational.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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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 $A (2 a, 4 a), B (2 a, 6 a)$ and $C (2 a + a \sqrt{3}, 5 a)$ are the vertics of an equilateral triangle,then
$A B = \sqrt{(2 a - 2 b)^{2} + (6 a - 4 a)^{2}} = 2 a B C = \sqrt{(2 a + a \sqrt{3} - 2 a)^{2} + (5 a - 6 a)^{2}} = \sqrt{3 a^{2} + a^{2}} = 2 a A C = \sqrt{(2 a + a \sqrt{3} - 2 a)^{2} + (5 a - 4 a)^{2}} = \sqrt{3 a^{2} + a^{2}} = 2 a$
as $A B = B C = C A$
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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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+a√3,5a). Reason: In equilateral triangle all the coordinates of three vertices can be rational.

Assertion :If A(2a, 4a) and B(2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by $(2 a + a \sqrt{3}, 5 a) .$ Reason: In equilateral triangle all the coordinates of three vertices can be rational.