Question

The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.

Answer 1

In an equilateral triangle, the height ‘h’ is given by

Here it is given that ‘PQ’ forms the base of two equilateral triangles whose side measures ‘2a’ units.

The height of these two equilateral triangles has got to be

In an equilateral triangle the height drawn from one vertex meets the midpoint of the side opposite this vertex.

So here we have ‘PQ’ being the base lying along the y-axis with its midpoint at the origin, that is at (0, 0).

So the vertices ‘R’ and ‘R’’ will lie perpendicularly to the y-axis on either sides of the origin at a distance of ‘’ units.

Hence the co-ordinates of ‘R’ and ‘R’’ are