MATHEMATICS LAB · GEOMETRY

Geometric Loci and Constructions in the Plane

Move points and lines to explore perpendicular bisectors, angle bisectors, conics defined by distances and families of lines. Observe their properties as you change the inputs.

Coordinates are real numbers measured in arbitrary units (u), and angles are given in degrees. Points can be dragged; degenerate configurations are reported rather than fabricated.

2. Interactive construction

Cartesian axes with equal scales

Grid Distances and auxiliary constructions Labels

Drag points A, B, V, F or Q to change the construction. Drag the background to pan; use the wheel or + and − to zoom. Animate P automatically scrolls the graph into view.

Figure or locus Main construction Point P and centers Distances and auxiliaries

3. Understanding the construction

4. Results

Live updates

5. Step-by-step calculations

Constructions and checks

What you can explore

Equal distances

Perpendicular bisectors, angle bisectors, focal loci and distance ratios between fixed points.

Conics as loci

Parabola, ellipse and hyperbola defined through distances and geometric constructions.

Families of lines

Pencils of concurrent lines and families of parallel lines, with selectable members.

Constructions use numerical Euclidean plane geometry. Degenerate cases are handled through explicit conditions and numerical tolerances; curves are displayed by sampling.