1. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 7-6-EXT Segment Partition Holt Geometry Lesson Presentation Lesson Presentation Holt McDougal Geometry

2. 7-6-EXT Dilations and Similarity in the Coordinate Plane Divide a directed line segment into partitions. Objectives

3. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane Directed line segment Vocabulary

4. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 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.

5. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 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.

6. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 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: 2 3 2 3 2 3 2 3 of rise = 6 = 4 2 3 2 3 of run = 9 = 6

7. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane Example 1 Continued Point Q is 4 units down and 6 units right from R. Its coordinates are Q(3, –1).

8. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 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

9. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 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: 3 10 3 of rise = 10 = 3 3 10 3 of run = 10 = 6 Point Q is 3 units down and 6 units right from R. Its coordinates are Q(4, 1).

10. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 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. Point G divides the segment in the ratio 1 to 3 from A to B. A D E F C G H I B

11. Holt McDougal Geometry 7-6-EXT Dilations and Similarity in the Coordinate Plane 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. A D E F G B C P