Directed Line Segments and Modeling Answers

What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio?

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What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary.

-5.2 2.9✔ 5.28.9

Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.

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Analyze the student’s work. Is the answer correct? Explain.

What are the coordinates of point P on the directed line segment from R to Q such that P is the length of the line segment from R to Q? Round to the nearest tenth, if necessary.

In the coordinate plane, the directed line segment from K to N has endpoints at K(–6, –2) and N(8, 3). Point L partitions the directed line segment from K to N in a ratio of 1:2. Point M partitions the directed line segment from L to N in a ratio of 3:1. What are the coordinates of point M? Round to the nearest tenth, if necessary.

Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.