1. 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. At the end of this lesson, you should be able to answer the following question: How do you find the point on a directed line segment that partitions the segment in a given ratio?

2. Vocabulary Directed Line Segment: has a starting point and a end point, a direction. To partition a directed line segment is to divide it into two segments with a given ratio.

3.  A ratio is a comparison of two quantities  The ratio of a to b can be expressed as: a : b or a / b or

4. Connor has a wallet with: 1-$20 bill 2- $10 bills 1- $5 bill 8-$1 bills 1)What is the ratio of $1 bills to $10 bills? 8:2 or 8/2 or 4/1 or 4:1 2) What is the ratio of $10 bills to the total number of bills in the wallet? 2:12 or 2/12 or 1/6 or 1:6

5. A 32 foot long piece of rope has a knot tied to divide the rope into a ratio of 1:1. 32 ft Where should the knot be tied? 1.Divide the rope into 8 sections 2.32ft divided by 8 is 4ft 3.There should be 1 unit in the first partition for every 1 unit in the 2 nd 4.If the ratio is 1:1, then there is the same amout on each side of the partition. 4:4 is the same as 1:1 5.The knot should be tied at 16 feet 6.A 1:1 ratio is the mid point AB 4 8 12 16 20 24 28 32

6. How do we find mid point if we are given two coordinates?

7.  Used to find the center of a line segment if you are given the coordinates of the 2 ends

8.  S tack em  A dd em  D ivide by 2 (4, 8 ) (1, 12) (5, 20) 2 2 (2.5, 10) Find the midpoint between A(4,8) and B(1,12)

9.  Find the midpoint between:  1) A (-4, 5) and C(3, -4) S A D2D2

10.  Find the midpoint between:  2) A (-3, -4) and C(6, -5) S A D2D2

11. Ex. In segment A is (4, 5) and the mid point is B(10, 12). Find the endpoint C We can still use SAD 2, But we have to work it backwards and opposite.

12. 1. In segment A is (4, 5) and the mid point is B(10, 12). Find the endpoint C We can still use SAD 2, But we have to work it backwards and opposite. 1. Multiply m.pt by 2 2. Subtract the end 3. That is your end 4. Check it D2D2 A S M2M2 S I cant use SAD 2 Because there is nothing to add the end point to….

13. 2. In segment A is (6, -5) and the mid point is B(-3, -4). Find the endpoint C D2D2 AS M2M2 S Remember, if they give you a midpt, use SAD, but backwards and opposite, also make sure you start with the mid point

14. Point P divides in the ratio 3 to 1. 1. What does this mean ?  There are 3 units between A and P for every 1 unit between P and B

15. A 32 foot long piece of rope has a knot tied to divide the rope into a ratio of 3:5. 32 ft Where should the knot be tied? 1.Divide the rope into 8 sections 2.32ft divided by 8 is 4ft 3.There should be 3 units in the first partition for every 5 in the 2 nd 4. The knot should be tied at 12 feet AB 4 8 12 16 20 24 28 32

16. Finding a point that partitions a segment into a specific ratio Given the points A(-1,2) and B(7,8), find the coordinates of the point P on the directed line segment AB that partitions AB into the ratio 1:1 *Start with the end, B Ratio of 1:1 is same as midpoint. But watch what we Do with the ratio… S A D

17. Finding a point that partitions a segment into a specific ratio Given the points A(-1,2) and B(7,8), find the coordinates of the point P on the directed line segment AB that partitions AB into the ratio 1:3 *Start with the end, B We can use SAD, but have to adjust it for the ratio. S A D

18. Finding a point that partitions a segment into a specific ratio 2. 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 2:3 *Start with the end _____ We can use SAD, but have to adjust it for the ratio. S A D