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# 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. - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### 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.

#### Solution

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)`

Is there an error in this question or solution?

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Solution 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. Concept: Concepts of Coordinate Geometry.
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