draw the figure in which triangles ABC and ADC are equilateral triangles on common base AC each side of triangle beng 2a units.

vertices A and C lie on the x- axis and vertices B and D lie on y- axis. O is the midpoint of AC and BD. find the coordinate point of B

please please please answer this query within 3 hrs. tomorrow is my maths test

Answer :

Given  

ABC and ADC are equilateral triangles with same base AC ,
And length of each side   =  2a unit 
SO,
AB  = BC   =  AC   =  AD   =  DC   =  2a  unit

And As given O is the middle point of AC and BD , SO,

OA  =   OC   =  a   unit 

In triangle AOB we apply Pythagoras theorem and get 

AB²  = OA²  + OB² 

OB²  = ( 2a )²  - a²                                      ( As we know AC   =  2a  and OA   =  a  unit )

OB²  = 4a²  - a²

OB²  =  3a²

OB   = $\sqrt{3}$ a  unit  

SO coordinate at B =  ( 0 , ​$\sqrt{3}$ a  )                                (  Ans )