The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin.find vertices of the triangle.

Dear student,

here's the answer.

ATQ,

the coordinates of the vertex on the y axis are (0,a) and (0,-a)

since the mid point of the base is at the origin, so the perpendicular bisector of the base has to pass thru the origin and must lie along the x axis.9at right angles to the base)

so if BC is the base and A is the third  vertex, then coordinates of A must be (a,0) or( -a,0)..using the distance formula and the given info that side of the triangle=2a

so the vertices are

(0,a),(0,-a),(a,0)

or

(0,a)(0,-a),(-a,0)