the base BC of an equilateral triangle ABC lies on y-axis.The co-ordinates of the point C are (0,3).If the origin is the mid-point of the base BC, fin the coordinates of point Aand B and hence find the area of ABC.

given ABC is an equilateral triangle. such that BC lies on y-axis.

and origin O is the mid-point of BC.

OC= 3 unit.

the point B will be at a distance 3 unit from O [since O is the mid-point ]

since B is on the y-axis.

the coordinates of B =(0,3)

BC=2*3=6 unit

clearly A will lie on x-axis

let the coordinates of A be (x,0)

therefore

hence the coordinates of A are 

and the coordinates of B are (0,3).

area of the equilateral triangle ABC =