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

`h =(sqrt3`("Side of the equilateral triangle"))/2`

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

`h = (sqrt3("Side of the equilateral triangle"))/2`

`= (sqrt3(2a))/2`

`h = asqrt3`

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 side of the origin at a distance of `asqrt3` units

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

`R(asqrt3,0)`

`R'(-a sqrt3, 0)`