Problem
GEO-B2-M05-P005 Line Through the Centre
#5
★★☆☆☆ Level 2 of 5
Prove that a line passing through the centre of inversion \(O\) maps to itself.
The image of point \(P\) lies on ray \(OP\).
If \(P\) lies on a line through \(O\), then ray \(OP\) lies on the same line. Therefore \(P'\) also lies on this line. This holds for every point, and inversion is its own inverse, so the whole line maps to itself.
It is important to distinguish this case from a line not passing through the centre.