Dividing Segments Proportionally

Find the point P that partitions the line segment AB given the ratio.
A (7, -2) B(4, 0) with the ratio 1:4

• (32/5, -8/5)
• (17/5, 2/5)
• (32/5, 22/5)
• (-13/5, 2/5)

Find the point P that partitions the line segment AB given the ratio.
A (-5, 8) B(9, 3) with the ratio 2:5

• (12, 11/7)
• (-1, 53/7)
• (-1, 46/7)
• (13, 11/7)

Find the point P that partitions the line segment AB given the ratio.
A (-6, -6) B(-2, 1) with the ratio 3:8

• (-54/11, 32/11)
• (-10/11, 32/11)
• (-54/11, -1/11)
• (-54/11, -45/11)

Find the point P that partitions the line segment AB given the ratio.
A (3, 5) B(4, 3) with the ratio 3:1

• (15/4, 5/2)
• (15/4, 7/2)
• (19/4, 3/2)
• (23/4, 3/2)

Given the points A(-1,2) and B(7,14), find the coordinates of the point P on directed line segment AB that partitions AB into a ratio 1:3. 

• (1,5)
• (3,7)
• (4,4)
• (5,8)

Given the points A(-2,4) and B(7,-2), find the coordinates of the point P on directed line segment AB that partitions AB in a the ratio 1:2. 

• (3,1)
• (4,3)
• (1,2)
• (0,1)

Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3.

In the above problem, what is the value of a/(a+b)?

• 1/3

• 1/4

• 3/1

• 3/4

Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3.

For the above problem, what is the value for the x-component and y-component?

• (6, 12)

• (6, 16)

• (8, 12)

• (8, 12)

Number Line Problem:

Find the point B that will divide the segment AC in a 4:1 ratio. Point A is at -3 and Point C is at 7.

• 5

• -1

• 1

• 3

Given the points A(-2,4) and B(7,-2), find the coordinates of the point P on directed line segment AB that partitions AB in a the ratio 1:2. 

• (3,1)
• (4,3)
• (1,2)
• (0,1)