Directed Line Segments and Modeling Answers

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?

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).

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).

Point P partitions the directed line segment from A to B into the ratio 3:4. Will P be closer to A or B? Why?

On a number line, the directed line segment from Q to S has endpoints Q at –8 and S at 12. Point R partitions the directed line segment from Q to S in a 4:1 ratio.Which expression correctly uses the formula to find the location of point R?

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).

On a coordinate plane, a line is drawn from point A to point B. Point A is at (7, negative 2) and point B is at (negative 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?

On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).

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).