Y over X Views: Ratio-Based Geometric and Set Exploration

This GeoGebra example presents a dynamic view centered on the ratio y/x, illustrating how the quotient of two variables generates geometric loci and set relationships. It demonstrates the interplay between two-dimensional vectors, right triangles, set theory (intersections), curve sketching, and combinatorial counting. The construction uses the IntersectPath command on objects a, n, p, and equation eq1 to compute intersection paths that reveal points or curves satisfying specific ratio conditions. Suitable for high school and above, this resource helps students grasp concepts like slope, similar triangles, set operations, and parametric curves, while encouraging cross-disciplinary thinking between algebra and geometry.