Using Matrices for Transformations

① This example demonstrates how to apply matrix-based linear transformations to plane figures such as triangles and quadrilaterals, showing the resulting changes in position and shape. ② The core mathematical concepts are matrix multiplication and geometric transformations (including rotation, scaling, shearing), as well as the application of matrices in coordinate transformations. ③ Construction highlights: based on the construction summary, it uses GeoGebra commands Segment and ApplyMatrix, creating original objects a, b, c, d and matrix M_1, then generating transformed points A', B', C', D', along with auxiliary segments f, g, h, i and text1 for labeling and explanation. ④ Suitable for high school or early college students learning linear algebra and analytic geometry, and for teachers demonstrating the visual effects of matrix transformations in class.