1. Lesson 5: Partitioning a Directed Segment
(1, 10)
(12, 10)
(9, 9)
(11, 5)
DO NOW:
(6.5, 10)
Coordinates?
(10, 7)
Coordinates?

2. C. Town A is located on a coordinate grid at (3, 10) the midpoint between town A and town B is (7, 9). Find the coordinates for town B.

3. Page 24

8. A directed line segment represents the horizontal & vertical movement(s) necessary to get from one endpoint to the other.

9. Example:
Example:
The directed line segment CD represents movement to the right (2) & down (4) from C to D.

10. Remember: Ratio = Fraction
If we graphed the midpoint of CD and labeled it L, what would be the ratio of the lengths of the 2 segments we created?
Remember: Ratio = Fraction

11. What is the ratio of CL to CD? 1:1
1:2
(or ½)
What is the ratio of CL to CD?
1:1
Since L is the midpoint of CD, what is the ratio of CL to LD? L

12. What if we wanted to place a point on a segment, so the segments created are in a ratio other than 1:1 (midpoint)?

13. What does the ratio AP:PB = 1:2 actually mean?
Find the coordinates
of point P along the directed line segment AB so that the ratio of AP to PB is 1 to 2.
What does the ratio AP:PB = 1:2 actually mean?
AP = ½ (PB) or PB = 2(AP)
Point P must be placed on AB to satisfy this requirement.

14. Label P as (x, y) Label A(3, 2) as (x1, y1) Label B(6, 8) as (x2, y2)
Find the coordinates
of point P along the directed line segment AB so that the ratio of AP to PB is 1 to 2.
(X2, Y2)
(X1, Y1)
Label P as (x, y)
This is what we’re finding
Label A(3, 2) as (x1, y1)
This is what
we’re given
Label B(6, 8) as (x2, y2)
Make a fraction
from the given ratio
1 to 2 = ½

15. Plug x values into the formula: x - x₁ = The Given Ratio (fraction)
Find the coordinates
of point P along the directed line segment AB so that the ratio of AP to PB is 1 to 2.
(X2, Y2)
(X1, Y1)
Plug x values into the formula:
x - x₁ = The Given Ratio (fraction)
x₂ - x
x – = 1
6 – x
(Use the Cross Products Property to multiply)

16. Cross multiply and solve: 2(x – 3) = 1(6 – x) 2x – 6 = 6 – x 3x = 12
Find the coordinates
of point P along the directed line segment AB so that the ratio of AP to PB is 1 to 2.
(X2, Y2)
(X1, Y1)
x – = 1
6 – x
Cross multiply and solve:
2(x – 3) = 1(6 – x)
2x – = 6 – x
3x = 12
x = 4

17. Plug y values into the formula: y - y₁ = The Given Ratio y₂ - y
Find the coordinates
of point P along the directed line segment AB so that the ratio of AP to PB is 1 to 2.
(X2, Y2)
(X1, Y1)
Plug y values into the formula:
y - y₁ = The Given Ratio
y₂ - y
y – = 1
8 – y

18. The coordinates of P are: (4, 4)
Find the coordinates
of point P along the directed line segment AB so that the ratio of AP to PB is 1 to 2. P
y – = 1
8 – y
Cross multiply and solve:
2(y – 2) = 1(8 – y)
2y – = 8 – y
3y = 12
y = 4
The coordinates of P are: (4, 4)

19. x – (-6) = 2 y – (-5) = 2 4 – x 3 0 – y 3 x + 6 = 2 y + 5 = 2
Find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 2 to 3.
A(−6, −5), B(4, 0)
(x1, y1)
(x2, y2)
Fraction = 2/3
x – (-6) = y – (-5) = 2
4 – x – y
x + 6 = y + 5 = 2
4 – x – y
3(x + 6) = 2(4 – x) (y + 5) = 2(– y)
x = – y = – 3
Point P is (-2, -3)

20. Tonight’s HW #5
Big Ideas
p22: Monitoring Progress 5, 7
p156: Monitoring Progress 1
pp 160: 1, 4 & 6