Presentation is loading. Please wait.

Presentation is loading. Please wait.

Lesson 5: Partitioning a Directed Segment

Similar presentations


Presentation on theme: "Lesson 5: Partitioning a Directed Segment"— Presentation transcript:

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

4

5

6

7

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


Download ppt "Lesson 5: Partitioning a Directed Segment"

Similar presentations


Ads by Google