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Bell Work

Learn how to find the point on a directed line segment between two given points that partitions the segment in a given ratio. Understand slope and use the segment partitioning formula.

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Bell Work

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  1. Bell Work

  2. CC Standard G-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Objective: Students will be able to: find the point on a directed line segment that partitions the segment in a given ratio. Partitioning a Segment

  3. Understanding Slope • If a line rises as you move from left to right, then the slope is positive. Riding a bike uphill

  4. Understanding Slope • If a line drops as you move from left to right, then the slope is negative. Skiing Downhill

  5. Understanding Slope • A horizontal line has zero slope: m = 0 Running on a flat surface like a track Or any athletic field Running on a flat surface like a track Or any athletic field Running on a flat surface like a track Or any athletic field

  6. Understanding Slope • A vertical line has no slope: m is undefined. Running into a wall, you cant get past it Running into a wall, you cant get past it

  7. y2–y1 x2–x1 Slope Formula The slope of a line through the points (x1, y1) and (x2, y2) is as follows: m =

  8. y2 – y1 = x2 – x1 6 – (–3) 9 3 4 – (–2) 3 The slope of the line that passes through (–2, –3) and (4, 6) is . 2 6 2 = = Ex. Find the slope of the line that passes through (–2, –3) and (4, 6). Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6). Substitute 6 for y2, –3 for y1, 4 for x2, and –2 for x1. *** Always reduce your fractions****

  9. What is a ratio? • A ratio is a comparison of two quantities • The ratio of a to b can be expressed as: a:b

  10. Segment Partitioning Formula

  11. Example 1: Find the coordinate of point P that lies along the directed line segment from A(3, 4) to B(6, 10) and partitions the segment in the ratio of 3 to 2. Directed Line Segment: Tells the direction in which from which point to start and end. In this case, from Point A to Point B What does that tell you about the distance AP and PB in relation to AB?

  12. example 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 2:1. • Find the run and rise for RS 2. Multiply the rise by the ratio from R to Q, and the run by the ratio of R to Q 3. Add/subtract these values to your startingpoint R

  13. example 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 3:7.

  14. example Find the coordinates of the point P that lies along the directed segment from A(2, 2) to B(7, -3) and partitions the segment in the ratio of 1:4

  15. Example Find the coordinates of point P that lies along the directed line segment from M to N and partitions the segment in the ratio of 3:2

  16. 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 (3, -1)

  17. Try One! Find the point M that is 2/5 of the way along the directed line segment from point A(–3, 3) to point B(2, –7). (-1,-1)

  18. Your Turn… Find the point M along the directed line segment from point A(–3, 9) to point B(13, –1) that divides the segment into the ratio 1:3. (Hint: M is closer to B… so really you are doing a 3:1 ratio, so this changes your fraction!) Answer: (9, 1.5)

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