CC Standard G-GPE.6 Find the point on a directed line Segment between two

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?

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.

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

Connor has a wallet with: 1-$20 bill 2- $10 bills 1- $5 bill 8-$1 bills 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

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

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

Midpoint Formula • Used to find the center of a line segment if you are given the coordinates of the 2 ends

SAD STACKERA way to remember the midpoint formula • Find the midpoint between A(4,8) and B(1,12) (4 , 8 ) (1, 12) (5, 20) 2 2 (2.5, 10) • Stack em • Add em • Divide by 2

S YOU TRY!! A • Find the midpoint between: • 1) A(-4, 5) and C(3, -4) D2

S YOU TRY!! A • Find the midpoint between: • 2) A(-3, -4) and C(6, -5) D2

What if they give you a mid pointand an end point, how can we findthe other end point? Ex. In segment A is (4, 5) and the mid point is B(10, 12). Find the endpoint C We can still use SAD2, But we have to work it backwards and opposite.

S A 1. In segment A is (4, 5) and the mid point is B(10, 12). Find the endpoint C We can still use SAD2, 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 I cant use SAD2 Because there is nothing to add the end point to…. D2 M2 S

S A D2 M2 2. In segment A is (6, -5) and the mid point is B(-3, -4). Find the endpoint C Remember, if they give you a midpt, use SAD, but backwards and opposite, also make sure you start with the mid point S

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

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

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 Finding a point that partitions a segment into a specific ratio S A Ratio of 1:1 is same as midpoint. But watch what we Do with the ratio… D

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 Finding a point that partitions a segment into a specific ratio S A We can use SAD, but have to adjust it for the ratio. D

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 _____ Finding a point that partitions a segment into a specific ratio We can use SAD, but have to adjust it for the ratio. S A D

CC Standard G-GPE.6 Find the point on a directed line Segment between two