Translations of Lines Through the Origin - Tool

This example demonstrates the translation of lines passing through the origin in a coordinate system. It involves core mathematical concepts such as translation, parametric curves, symmetry, congruence, dilation, and 3D vectors. The construction uses GeoGebra commands like Textfield, LaTeX, TableText, and objects including m_1, b_1, c_1, m, b, c, a, text1, button4_1, button4_2, button5, button6, button7, functionf, functiong, InputBox6, f_1, f_2, text2, text3, A1, B1, C1, n, n_1, n_2, InputBox1, d, m_2, text7, b_2, c_2, f_3, text8, e, InputBox2, InputBox3, InputBox4, D1, text4. It is suitable for high school mathematics teaching and the study of geometric transformations.