A is at -1, and B is at -7.Find the point, T, so that T partitions A to B in a 2:1 ratio.

Warm up

A is at -2, and B is at -7.Find the point, T, so that T partitions A to B in a 2:1 ratio.

Warm up - 2

2 1 1( )

ax x x

a b

Review HW

Find a Point that Partitions a Segment in a

Given Ratio a:b

2 1 1 2 1 1,a a

x x x y y ya b a b

Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 2.

In order to divide the segment in the ratio of 3 to 2, think of dividing the segment into 3 + 2 or 5 congruent pieces.

A(3, 4), B(6, 10); 3 to 2.

AB has a rise of 6.

6

AB has a run of 3.

3

A(3, 4), B(6, 10); 3 to 2.

To find the coordinates of point P…

6

3

1 1, a a

run x rise ya b a b

3 33 3, 6 4

5 5

4.8, 7.6

Example 1: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(1, 3), B(8, 4); 4 to 1.

2 1 1 2 1 1, a a

x x x y y ya b a b

4 47 1, 1 3

5 5

6.6, 3.8

Example 2: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, 1), B(4, 5); 3 to 7.

2 1 1 2 1 1, a a

x x x y y ya b a b

3 36 2, 4 1

10 10

0.2, 2.2

Example 3: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(8, 0), B(3, -2); 1 to 4.

2 1 1 2 1 1, a a

x x x y y ya b a b

1 15 8, 2 0

5 5

7, 0.4

Example 4: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2.

2 1 1 2 1 1, a a

x x x y y ya b a b

3 38 2, 5 4

5 5

2.8, 1

New York Task

CW/HW