Exercise 9: Integrated Exploration of Linear Functions and Geometry

① This example demonstrates a comprehensive mathematical exercise combining linear functions, squares, conic sections, perimeter, linear programming, and confidence intervals through an interactive GeoGebra environment. ② Core concepts include properties of linear functions, geometric attributes of squares, equations and graphs of conic sections, perimeter calculations, feasible regions and optimal solutions in linear programming, and statistical confidence intervals. ③ Construction highlights: from the summary, commands such as Random, RandomElement, Textfield, TableText, and Mirror are used; objects include multiple lines (m, a, d_1, a_1, c, f_1, b, g, h, f, b_1, p, l, e, k, d, i, n, c_1), points (A1, A1_1, B1_1, C_1, D_1, B_1), a button (button1), text elements (text1, text3_1), and circles (o, o'). ④ Suitable for high school or early college students as a cross-topic review, and for teachers to design inquiry-based assignments that reveal connections among different mathematical areas.