# The base BC of an equilateral triangle ABC lies on y axis. The coordinates of pt. C are (0,-3). If the origin is the mid pt. of the base BC, find the coordinates of the pt. A and B and hance find the area of the triangle.

given: ABC is an equilateral triangle . BC lies on y-axis and origin is the midpoint of BC.

let the coordinates of B are (0,y), since it lies on y-axis

therefore the coordinates of B are y-3/2=0 i.e. y=3 coordinates are (0,3)

therefore BC = 3-(-3)=3+3=6 units

OA is the perpendicular bisector of BC therefore the vertex A will lie on OA i.e. x-axis

let the coordinates of A are (x,0). since ABC is an equilateral triangle

AB = BC

thus the coordinates of A are

area of the equilateral triangle ABC =

hope this helps you

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