Question

The adjoining figure shows an equilateral triangle OAB with each side = 2a units. Find the coordinates of the vertices.

Answer 1

If we draw a perpendicular from vertex $A$ to X-axis the foot of the perpendicular is the mid-point of $OB$

So, the x-coordinate of $A=\frac{1}{2}\left(2a\right)=a$

y-coordinate of $A=$ Height of an equilateral triangle $=\frac{\sqrt{3}}{2}a$

Co-ordinates of $A=(a,\frac{\sqrt{3}}{2}a)$

Co -ordinates of $B=(2a,0)$

Co-ordinates of $O=(0,0)$