Directed Line Segment Geometry

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(-3,-5) and B(5,0), find the coordinates of the point P on directed line segment AB that partitions AB in a the ratio 2:3. 

• (0.5,-2.2)
• (0.2,-2.4)
• (1/5, -5/2)
• (0,-2)

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

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

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

Find point P along the directed line segment from point A(18,-2) to B(0,6) that divides the segment in a ratio of 1 to 3.

• (-9/2 , 4)
• (-27/2 , 0)
• (-13/4 , 0)
• (-9, 2)

Which point P on XY partitions the directed line segment from X to Y in the ratio of 4 to 1?

• (-2.6 , 1.6)
• (-2.25 , 1.75)
• (1.25 , 3.25)
• (1.6 , 3.4)