Question
Sat February 19, 2011

# 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, find the coordinatesof the vertices of triangle ABC

Sat February 19, 2011
Dear student,

It is given that the base BC lies on x-axis. So, the y coordinate of the points B and C will be 0.
It is also given that the vertex B is at the origin. So, the coordinates of the vertex B are (0, 0).
The length of the sides of the equilateral triangle is a units.
So, the coordinates of the point C are (a, 0).
[Since, BC = a units and coordinates of B are (0, 0)]

Let the coordinates of the point A be (x, y).
Now, AB = AC = a units
So, by using distance formula,
AB2 = x2 + y2 = a2   (1)
AC2 = (x - a)2 + y2 = a2    (2)
Using (1) in (2), we get
We hope that clarifies your query.
Regards,
Team
TopperLearning
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