Linear Interpolation for f(8): Trapezoid and Similar Triangles

This example demonstrates how to estimate the value of a function at x=8 using linear interpolation, visualized through a trapezoid and similar right triangles. The core mathematical concepts include linear interpolation, linear functions, proportional relationships in similar triangles, and properties of trapezoids. The construction uses GeoGebra commands Segment and Midpoint, building on known points A and B to create segment g, with midpoints C and D to form similar triangles that determine the interpolated value. Suitable for middle school to high school students learning function approximation, and useful for classroom activities connecting geometry and algebra.