# the base BC of an equilateral triangle ABC lies on y-axis. the coordianates of point C are (0,-3). the origin is the mid-point of the base. find the coordinates of the points A and B. also find the coordinates of another point D such that BACD is a rhombus.

Given base BC of equilateral triangle ABC is lies on y - axis ,
And
Coordinates of C ( 0 , -  3 )  and Origin is the mid point of line BC , So, Coordinates of B ( 0 , 3 )

And Point A and D lies of x axis because we know axis are perpendicular to each other , So at origin x axis is perpendicular on y axis .
And
We know in equilateral triangle altitude also bisect opposite side . So we get Coordinates of A (  x  ,  0 )
And we know Diagonals of rhombus are perpendicular bisectors to each other , So
Coordinate of D ( - x  , 0 )

As :

we know
Distance formula d  =
So,
Side of BC  =
As given ABC is equilateral triangle , So

AB  =  BC  =  CA , So

AB  = , So
we get

So,
Coordinates of A ( 5 , 0 )  and Coordinates of D ( - 5 , 0  )                                   ( Ans )

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