Ruler and Compass Construction 26
Mirror Reflection of a Ray Between Two Given Points

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1. Arbitrary point A on the line
2. Arc centered at A, through C
3. Arbitrary point B on the line
4. Arc centered at B, through C
5. Mirror point D
6. Segment DE
7. Reflection point F
8. Ray path CFD

The reflected ray appears from E to go straight to the mirror image point of C, so
simply construct the mirror image point of C and draw a line to it from E.