If ‘ a  ‘ is the length of one of the sides of an equilateral triangle ABC,   base BC   lies on x-axis and vertex B   is at the origin, then from the following choices, the coordinates of the vertices of the triangle A,B,C   is:

If '  ' is the length of one of the sides of an equilateral triangle   base   lies on x-axis and vertex   is at the origin, then from the following choices, the coordinates of the vertices of the triangle   is:

1. A

2. B

3. C

4. D

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Solution:

Given that, '  ' is the length of one of the sides of an equilateral triangle ABC.
.
The distance formula between two points   is given by,

Since the length of an equilateral triangle is ‘a’ and BC lies on x-axis, so the y-coordinate will be zero.
And, x = x.
Since, B is at the origin, C is the point C(x, 0).
We know that, BC = a.
Here,

So, the coordinate of C is (a, 0).
Put  .

Put  , so that the coordinate of A be  and C is  , we get,
Substitute the value of (2) in (1), we get,

The coordinate is   .
Hence, option 3) is correct.

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