# In fig triangle, ABC is an equilateral triangle with coordinates of b and c as b(1,0) and c(5,0). Find the coordinates of vertex A.

Since, A lies above x - axis , so coordinates of A are : $\text{A}\left(3,2\sqrt{3}\right)$

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The ordinates of both B & C are 0.
So, BC= (abscissa of B−abscissa of C)=(5−1)=4units=a
The side of equilateral ΔABC.
∴  Its height=23​​a=23​​×4=23​ units.
Also, the mid point of BC=(25+1​,20+0​)=(3,0).
Now, ΔABC is equilateral and BC is on the x-axis.
So, the abscissa of A will be the mid point of BC.
The ordinate of A will be the height of ΔABC from the mid point of BC.
∴ The coordinates of A are (3,2√3).

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