Download - 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 -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