Pyramid Passing Through 2 – 3D Geometry and Matrix Transformations

This GeoGebra example demonstrates a pyramid (solid with polygonal base) passing through a plane, visualized through dynamic 2D projections and geometric transformations. It illustrates how a 3D solid intersects a plane, showing cross-sections and the effects of scaling and translation. Core math concepts include solid geometry (pyramids, plane sections), similarity and ratios, and matrix transformations (dilation, translation) applied to coordinates. Construction uses GeoGebra commands: Polygon to build the base, Distance to measure side lengths, Dilate to scale points (creating the apex or cross-section), Line and Intersect to construct auxiliary lines and intersection points. Multiple objects (A, B, poly1, a, b, c, C, distanceBA, TextBA, d, A', e, D, poly2, a', b_1, c_1, d_1) are linked to create an interactive animation. Suitable for high school or early college students learning 3D geometry, cross-sections, and the geometric meaning of matrix transformations, as well as for teachers designing interactive geometry lessons.