Perpendicular Bisector
I built a version of this in Desmos in 7th grade for a class project. The assignment was basically "make something with geometric constructions" and I went way too deep into it.
Here's what it does: you've got two line segments (drag the blue points). The tool finds the midpoint of each segment, draws a line connecting those two midpoints, then finds the perpendicular bisector of THAT new line.
What I think is cool about it: all four of the original points are completely random, but the perpendicular bisector is perfectly determined by them. No matter where you drag the points, the math gives you exactly one answer. Drag them fast and watch the bisector snap into place in real time.
Try getting the two original segments to be parallel — see what happens to the bisector.
Drag the Points
Drag the blue points to move them
What I Keep Coming Back To
The reason this ended up as my Desmos project is that it felt like a trick. You give me four random points and I can derive this very specific line from them. The perpendicular bisector shows up in real geometry problems — it's how you find the center of a circle from three points on its edge, which is how engineers fit curves to roads and bridges.
What I'm still working out: the relationship between the original two segments and the bisector isn't obvious. Change just one point and the whole bisector jumps. I want to understand that sensitivity better.