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 co-ordinates of the vertices R and R' of a triangle

Answer 1

Since midpoint of PQ is the origin and PQ=2a
Therefore, OP=OQ=a

Here the coordinates of P and Q are (0,a) &(0,-a) respectively.
Since ∆PQR and ∆PQR' are equilateral.
Therefore, their third vertice R and R' lie on the perpendicular bisector of PQ.
X'OX is perpendicular bisector of base PQ.
Thus R and R' lie on X-axis
therefore their Y coordinate are zero.


In ∆ROP
OR^2 +OP^2=PR^2
OR^2+a^2=(2a^2)
OR^2=3a^2
OR=√3a

Similarly ,OR'=√3a
Thus coordinate of vertices R and R' are(√3a,0) and (-√3a,0) respectively.



Hope it help!!

Answer 2

Answer:R(√3a,0),R'(-√3a,0)

This is the answer