Rectangular Components in Rotated Coordinates

① This example visualizes the rectangular components (orthogonal projections along new axes) of a vector or point in a rotated coordinate system, clarifying how coordinate rotation affects component decomposition. ② Core mathematical concepts include coordinate transformation, orthogonal projection, vector decomposition, trigonometric functions (tangent), parallelogram law, along with auxiliary constructions involving equilateral triangles and geometric mean. ③ Construction highlights: using GeoGebra commands such as Intersect, Point, Circle, Line, OrthogonalLine, Distance, Segment, Vector, Polygon, Angle, and Sequence to create rotated axes, projection lines, component vectors, parallelograms, and angle labels, with sliders (step, n) and text objects (text1, text2, text3) for dynamic interaction. ④ Suitable for high school or early college students learning analytic geometry, vector algebra, and coordinate transformations, as well as for teachers demonstrating component decomposition in rotated frames.