GEO.1.4

Uses a real-world scenario involving a mall, library, and home locations to demonstrate how to apply these partitioning techniques to coordinate geometry problems.

Defines a directed line segment as a line segment with an associated direction, identifying an initial point (x1, y1) and a terminal point (x2, y2), along with their horizontal (run) and vertical (rise) components.

Demonstrates how to calculate horizontal components by finding the difference between x-coordinates (x2 - x1) and vertical components through the difference of y-coordinates (y2 - y1).

Explains partitioning a segment into congruent parts and distinguishes between part-to-part ratios and part-to-whole ratios, which are essential for locating specific coordinate points.

Provides a step-by-step method for finding the location of point P on a directed line segment, including transforming part-to-part ratios into part-to-whole fractions.

Introduces the mathematical formula for partitioning segments when a graph is not available, using the ratio 'k' to find the coordinate point P.