[list=1][*]Draw a triangle [i]ABC[/i] and create point [i]D[/i] somewhere.[/*][*]Reflect [i]D[/i] about all sides of the triangle.[/*][*]All the mirror images of [i]D[/i] collinear? [color=#cccccc]Usually no.[/color][/*][*]Ask hints from GeoGebra where to put [i]D[/i] in order to have the mirror images collinear. [color=#cccccc]Type [code]LocusEquation[AreCollinear[D',D'₁,D'₂],D][/code].[/color][/*][*]Does this hint remind you of the [url=https://www.geogebra.org/m/EPCKjckB]Simson-Wallace theorem[/url]?[/*][*]Can you find a generalization of Simson-Wallace by using your discovery? [color=#cccccc]Yes, since both the mirror images and just the projections are collinear if [i]D[/i] is properly selected, it seems valid that any point on the line joining the mirror images and just the projections will result in something similar.[/color][/*][*]Can you find a special case of this conjecture to check the statement? [color=#cccccc]Yes, for example the projections can be mirrored on the mirror images, respectively. This can also be checked by using GeoGebra Automated Reasoning tools (namely, the Relation tool).[/color][/*][/list]