Envelope of bisector of a point and a line
Loading the math board and drawing, please wait…
This example demonstrates that the envelope of the bisector of a point and a line forms a parabola. It involves core mathematical concepts such as angle bisector, envelope, parabola, and coordinate geometry. The construction uses GeoGebra commands/objects like Line, Point, and LineBisector. It is suitable for high school students learning about the geometric properties and construction of parabolas.
GeoGebra Commands & Parameters
Line(A, B) → dPoint(d) → DLineBisector(F, D) → a
AI Drawing Prompt Reference
Draw a line d from point A to point B, then pick a point D on line d. Next, draw the angle bisector a of point F and point D. Finally, show the envelope of line a, which forms a parabola.
The prompt above was compiled from the original drawing commands and is for reference only.