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The base PQ of two equilateral …

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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.

Posted by Chirag Sood 5 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 2 months ago

Since the mid point of PQ is the origin and PQ = 2a

OP = OQ = a

Hence the coordinates of P and Q are (0,a) and (0,-a) respectively.

Since triangles PQR and PQR' are equilateral

Their third vertices R and R' lie on the perpendicular bisector of base PQ.

X'OX is the perpendicular bisector of base PQ.

Thus R and R' lies on X-axis,

their Y coordinates are zero.

In ROP, OR² + OP² = PR²

OR² + a² = (2a)²

OR² = 3a²

OR =

Similarly, =

Thus,the coordinates of the vertices R and are respectively.

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