Directed Line Segments and Modeling Answers

On a coordinate plane, a line is drawn from point A to point B. Point A is at (2, negative 3) and point B is at (negative 4, 9).

On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2).

Where will her cut be located? Round to the nearest tenth.

At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.

On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9).

What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?

If point P is of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 3, 1) and point K is at (negative 8, 11).

On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 8, negative 13) and point B is at (4, 11).

Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding the length of the directed line segment?