Switching Directions: Mirror Transformations for Integer Subtraction

This example demonstrates how “switching directions” in a geometric setting can change vector and point relationships, making the effect of integer subtraction visible in a concrete diagram. The key ideas are integers (especially subtracting integers), vector direction and magnitude, and using a mirror/reflection transformation to track how quantities change sign and outcome. Construction follows the GeoGebra workflow implied by the commands and objects: Point creates key points, Random provides randomized initial configuration, Vector builds the relevant vectors, and Textfield/Text annotate computed values. The Mirror command performs the reflection, while interactive elements such as button1/button2 and InputBox1 control inputs and update the scene. Typical objects include points labeled like A, B, C, D and auxiliary points, along with vectors (u, v) and text labels (e.g., d, D′, w) to visualize the “before vs. after” relationship. Suitable for middle and high school geometry/vector lessons, and for classroom explorations connecting arithmetic with transformations.