Geometric Construction and Algebraic Exploration of a Chessboard Inequality

This GeoGebra example demonstrates a chessboard inequality through dynamic geometric construction on a grid. It visually illustrates the relationship between polygonal regions, interior points, segments, perpendicular lines, and intersection points, revealing the geometric meaning of an algebraic inequality. Core mathematical concepts include inequalities, polygon area relations, point-in-polygon testing, orthogonality, and coordinate geometry. The construction uses GeoGebra commands Polygon, PointIn, Segment, OrthogonalLine, and Intersect, involving objects such as points O, A–H, polygons poly1/poly2/poly3, lines g/d/e/h, intersection points, and text labels. It is suitable for high school and introductory college algebra or analytic geometry courses, helping students cultivate multiple algebraic skills and geometric intuition through interactive visualization.