Locus: Equidistant from a Point and a Line

Loading the math board and drawing, please wait…

2017-12-18 14:13

In collections Locus

This example demonstrates the locus of a point maintaining equidistance from a fixed point and a fixed line. Key math concepts include equidistance, locus, coordinate geometry, and geometric construction. Construction highlights: using Segment to draw line segments, OrthogonalLine to create perpendicular lines, Intersect to find intersections, If for conditional logic, and Point to define moving points. Suitable for high school students learning about coordinate geometry and locus problems.

GeoGebra Commands & Parameters

Segment(A, P) → b
OrthogonalLine(P, a) → c
Intersect(c, a) → B
Segment(P, B) → d
If(abs(b - d) ≤ 0.02, P) → C
Point(a) → D
If(y(P) > -4, Angle[D, B, P]) → α

AI Drawing Prompt Reference

Draw a point P that is equidistant from a fixed point A and a fixed line a. First, draw line segment AP, then draw the perpendicular line c through point A to line a, find the intersection point B of line c and line a, next draw line segment PB, if the difference between the lengths of line segments AP and PB is less than 0.02, mark point P, finally, take a point D on line a and measure the angle DBP.

The prompt above was compiled from the original drawing commands and is for reference only.