Partitions of Line Segments

When do you use partitioning formula?

• to find the distance of a line segment

• to find only the midpoint of a line segment

• to find a point that divides a line segment into a specific ratio

• to shorten a line

Determine the ratio of the directed line segment AB

when partitioned by point P. (Hint: A is the initial point)

Determine the ratio of the directed line segment AB

when partitioned by point P. (Hint: A is the initial point)

Determine the ratio of the directed line segment AB

when partitioned by point P. (Hint: A is the initial point)

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Answer explanation

Remember, the directed line segment  $\overline{AB}$  means from A to B, no matter how they appear on the line. 

• P (4,0)

• P (6,0)

• P (3,0)

• P (8,0)

Answer explanation

If the ratio is 1:2, that means the scale factor is  $\frac{1}{3}$  . The run from 0 to 12 is 12 and the rise from 0 to 0 is 0. A third of 12 is 4 and a third of zero is zero.  Add the new run, 4, to the orignial x-value zero to get new x-value four, and add the new rise zero to the original y-value zero to get new y-value zero. 

• 1:2

• 2:1

• 3:1

• 1:3

Determine the ratio of the directed line segment AB

when partitioned by point P. (Hint: A is the initial point)