Transcript partitioning segments

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.


A ratio is a comparison of two quantities
The ratio of a to b can be expressed as:
a:b
or
a/
b
or
a
b
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
A 32 foot long piece of rope has a knot
tied to divide the rope into a ratio of 1:1.
A
4
8
12 16 20 24 28 32
B
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 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 1:1
5. The knot should be tied at 16 feet
6. A 1:1 ratio is the mid point
How do we find mid
point if we are given
two coordinates?

Used to find the center of a line segment if you
are given the coordinates of the 2 ends
 xx y y
midpoint  
,

2 
 2
• Find the midpoint between A(4,8) and B(1,12)
Stack em
Add em
Divide by 2
(4 , 8 )
(1, 12)
(5, 20)
2
2
(2.5, 10)
S
Find the midpoint between:
 1) A(-4, 5) and C(3, -4)

midpoint =  -.5,.5
A
D2
A(4,5)
C (3, 4)
(1, 1)
2 2
B(.5, .5)
S
Find the midpoint between:
 2) A(-3, -4) and C(6, -5)

A
D2
midpoint = 1.5, -4.5
A(3, 4)
C (6, 5)
(3, -9)
2 2
B(1.5, -4.5)
Ex. In segment AC
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. In segment AC
A is (4, 5) and the mid
point is B(10, 12).
Find the endpoint C
I cant
We
canuse
stillSAD
use2SAD2,
Because
there
is
But
we have
to work
it
nothing toand
add the
backwards
end point to….
opposite.
1. Multiply m.pt by 2
2. Subtract the end
3. That is your end
4. Check it
S
A
D2
, )
C (11,14)
A( 3, 4)
B(4,5)
(8,10)
S  A( 3, 4)
M2
C (11,14)
8 10
,
2 2
2. In segment AC S A D2
B
(

3,

4)
A is (6, -5) and the
mid point is
(6, 8)
M2
B(-3, -4).

A
(6,

5)
S
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
C(12, 3)
Point P divides AB 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.
A
4
8
12 16 20 24 28 32
B
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 2nd
4. The knot should be tied at 12 feet
Finding a point that
partitions a segment
into a specific ratio
Ratio of 1:1 is
same as midpoint.
But watch what we
Do with the 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
1 B( 7,8)
1 A( -1,2)
B( 7,8)
A( -1,2)
2
( 6,10) A
D
2 2
P( 3 ,5)
S
Finding a point that
partitions a segment
into a specific ratio
We can use SAD,
but have to adjust
it for the 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
1 B( 7,8)
3 A( -1,2)
B( 7,8)
S
A( -3,6)
4
( 4,14) A
D
4 4
P( 1,3.5)
Finding a point that
partitions a segment
into a specific ratio
We can use SAD,
but have to adjust
it for the 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
S
*Start with the end _____
2 S ( 6, 3) S ( 12, 6)
S
3 R( -3,3) R( -9, 9)
5
( 3, 3) A
D
5 5
P( .6, .6)