(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What is the easiest way of finding the symmetrical of a point relative to an arbitrary line?

(I was asked on an exam to find the symmetrical of a point relative to the line y = x, but that's rather trivial - just switch the coordinates. How can I do it for any arbitrary line ax + by = c?)

2. Relevant equations

3. The attempt at a solution

I found a way, but it's rather messy. Given the line s and the point P, find the line t that is perpendicular to s and passes through P. Calculate the distance d between P and s. Find the point on the line t that is also at a distance d from s.

This sounds awfully complicated and messy for me. Is there a quicker way?

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# Symmetric of a point relative to a line

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