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Partitioning a Segment

What does partition mean? To break apart into pieces!. 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 ratio of a partitioned line segment. Inquiry Question:

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Partitioning a Segment

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  1. What does partition mean? To break apart into pieces! 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 ratio of a partitioned line segment. Inquiry Question: How do you find the point on a directed line segment that partitions the segment in a given ratio? Partitioning a Segment Ratio: A comparison of 2 quantities.

  2. Point P divides in the ratio 3 to 1. • What does this mean? 2. Do you expect point P to be closer to A or closer to B? Why? 3. How does the slope of AP compare with the slope of the AB? Why?

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

  4. Ex. Find the slope of the line that passes through (–2, –3) and (4, 6). y2 – y1 = x2 – x1 6 – (–3) 3 9 4 – (–2) 3 The slope of the line that passes through (–2, –3) and (4, 6) is . 6 2 2 = = 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****

  5. 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 So point A must be labeled A and B What does that tell you about the distance AP and PB in relation to AB?

  6. Partitioning a segment • Label your points and Note: since it is a directed segment, order does matter. 2. Convert the ratio into a percent (keep as a fraction) a:b Percent ratio (%) 3. Find the rise and run for the segment (order does matter) Rise: Run: 4. To find the partitioning point: x – coordinate: x1-coordinate + run(% in fraction form) y - coordinate: y1 -coordinate + rise(% in fraction form)

  7. What is the ratio that segment AB is partitioned into a point by point P? • Focus on our y-intercepts. • AP: 4 - 8 = -4 • PB: 8-10 = -2 • *Our ratio has to be positive, so we use absolute value {-4} = 4, and • {-2} = 2 • 3. The ratio that segment AB is partitioned into a point by point P is 4:2 or 2:1 (5,8)

  8. Example: What is the ratio that segment AB is partitioned into a point by point P? B (4,6) P (0,4) A (-5,1)

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