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Divide a directed line segment into partitions.

Objectives. Divide a directed line segment into partitions. Vocabulary. Directed line segment. A directed line segment is a segment between two points A and B with a specified direction, from A to B or from B to A. To partition a directed line

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Divide a directed line segment into partitions.

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  1. Objectives Divide a directed line segment into partitions.

  2. Vocabulary Directed line segment

  3. A directed line segment is a segment between two points A and B with a specified direction, from A to B or from B to A. To partition a directed line segment is to divide it into two segments with a given ratio.

  4. Example 1: Finding the Coordinates of a Point in a Directed Line Segment Find the point Q along the directed line segment from point R(–3, 3) to point S(6, –3) that divides the segment into the ratio 2 to 1 First, find the rise and run of the directed line segment.

  5. Example 1 Continued rise = |3 – (–3)| = 6 run = |–3 – 6| = 9 Point Q is of the way between points R and S, so find of both the rise and the run: = 4 = 6 9 6 of rise = of run = 2 2 2 2 2 2 3 3 3 3 3 3

  6. Example 1 Continued Point Q is 4 units down and 6 units right from R. Its coordinates are Q(3, –1).

  7. Check It Out! Example 1 Find the point Q along the directed line segment from point R(–2, 4) to point S(18, –6) that divides the segment in the ratio 3 to 7. First, find the rise and run of the directed line segment

  8. Check It Out! Example 1 Continued rise = |4 – (–6)| = 10 run = |–2 – 18| = 20 Point Q is 3/10 of the way between points R and S, so find 3/10 of both the rise and the run: = 6 = 3 of rise = of run = 10 10 3 3 3 3 Point Q is 3 units down and 6 units right from R. Its coordinates are Q(4, 1). 10 10 10 10

  9. Example 2: Using Construction to Draw a Point in a Directed Line Segment Given the directed line segment from A to B, construct a point that divides the segment in the ratio 1 to 3 from A to B. C F E D A I H G B Point G divides the segment in the ratio 1 to 3 from A to B.

  10. Check It Out! Example 2 Draw a directed line segment from A to B, then construct point P that divides the segment in the ratio 2 to 3 from point B to point A. G C F E D A B P

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