First we construct a single transformed point.

 

Construct P*, which is a 90 degree rotation of P around O followed by a 2x dilation.

It is possible to solve this with compass and ruler alone. But the following procedure is easier. Construct in this order

  • The line through P and O.
  • The perpendicular to this line at O.
  • The fixed circle at O with radius 2*d(P,O).
The intersection of the circle and perpendicular line is the required point P*.

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