Point Coordinates on a Line: Intersection-Based Construction

This example demonstrates how to locate and represent the coordinates of multiple points lying on a single line using an intersection-based geometric construction. The key ideas are coordinate geometry (point coordinate representation), the geometric meaning of line relations, and how intersection points turn algebraic location into visible geometric information. Construction essentials: create lines with Line, compute intersection points with Intersect, generate the required Points, and optionally use Segment to illustrate the connecting line pieces. The figure includes several constructed points (e.g., B, C, E, F, H, etc.), line-related labeled objects (e.g., a, b, c, d and their variations), and a displayed label text4 for annotation. Suitable for middle school to early university levels, especially for teaching/learning coordinate placement, geometric construction, and graph-to-coordinate understanding.