CC Standard
G-GPE.6 Find the point on a directed line Segment between two given points that partitionsthe 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
quantitiesThe ratio of a to b can be
expressed as:
a : b or a/b or
b
a
Connor has a wallet with:
1-$20 bill2- $10 bills1- $5 bill8-$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
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 sections2. 32ft divided by 8 is 4ft3. There should be 1 unit in the first partition for every 1 unit in the 2nd
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 1:15. The knot should be tied at 16 feet6. A 1:1 ratio is the mid point
A B 4 8 12 16 20 24 28 32
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
midpoint ,2 2
x x y y
SAD STACKERA way to remember the midpoint formula
Stack em
Add emDivide by 2
(4 , 8 )
(1, 12)
(5, 20)
2 2
(2.5, 10)
• Find the midpoint between A(4,8) and B(1,12)
YOU TRY!! Find the midpoint between: 1) A(-4, 5) and C(3, -4)
midpoint = -.5,.5
( 4,5)
(3, 4)
A
C
S
A
D2
( 1, 1)2 2
( .5, .5)B
YOU TRY!! Find the midpoint between: 2) A(-3, -4) and C(6, -5)
midpoint = 1.5, -4.5
( 3, 4)
(6, 5)
A
C
S
A
D2
(3, -9)
2 2(1.5, -4.5)B
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.
AC
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
AC
D2
A
S
( 4,5)B
( , )C( 3, 4)A
M2 ( 8,10)S ( 3, 4)A
( 11,14)C
( 11,14)C
I cant use SAD2
Because there is nothing to add the end point to….
8 10,
2 2
2. In segment A is (6, -5) and
the mid point is B(-3, -4).Find the endpoint
C
AC D2AS
M2
( 3, 4)B
S
( 6, 8)
(6, 5)A
( 12, 3)C Remember, if they give you a midpt, use SAD, but backwards and opposite, also make sure you start with the mid point
Point P divides in the ratio 3 to 1.
1. What does this mean?
AB
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.
32 ft
Where should the knot be tied?
1. Divide the rope into 8 sections2. 32ft divided by 8 is 4ft3. There should be 3 units in the first partition for every 5 in the 2nd
4. The knot should be tied at 12 feet
A B 4 8 12 16 20 24 28 32
Finding a point that partitions a segment into a specific ratio
Given the points A(-1,2) andB(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
( 7,8)B( -1,2)A
1
1( 7,8)B( -1,2)A
Ratio of 1:1 is same as midpoint.But watch what weDo with the ratio…
2( 6,10)
S
A
D2 2( 3 ,5)P
Finding a point that partitions a segment into a specific ratio
Given the points A(-1,2) andB(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
( 7,8)B( -1,2)A
1
3( 7,8)B( -3,6)A
We can use SAD, but have to adjust it for the ratio.
4( 4,14)
S
A
D4 4( 1,3.5)P
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 _____
( 6, 3)S ( -3,3)R
2
3( 12, 6)S ( -9, 9)R
We can use SAD, but have to adjust it for the ratio.
5( 3, 3)
S
A
D5 5( .6, .6)P
S
