Perpendicular Lines and Slope: Open-Middle Construction

This example demonstrates, with an “open middle” setup, how to construct a perpendicular line from given geometric conditions and verify the slope relationship on a coordinate plane. It focuses on perpendicularity, slope (difference and slope), and the graphical meaning of linear functions, using logic to confirm whether the configuration satisfies the expected perpendicular/linear criteria. The construction uses PointIn to create the key points (e.g., a, b, c, d, e and A, B, C, D), Line to build the lines (including l1 and l2), Intersect to compute intersection points, and Angle to check right-angle behavior. Length is used to measure relevant segment quantities, while If provides conditional logic that triggers results and annotations (text1–text4 and button1). Angles (α) and auxiliary objects (c1, c2) support the verification. Suitable for middle/high school geometry-to-analytic-geometry transitions and classroom demonstrations of slope and perpendicular line reasoning.