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Partitioning a Line Segment Notes

Partitioning a line segment:

Directed line segment-segment between two points A and B with a specified direction, from A to B or from B to A.

Partitioning a segment divides it.

Ratio- Compares values. a:b or

To find a coordinate point, P, that partitions a segment:

Step 1: label x1, x2, y1, y2, because order matters!

Step 2: find run and rise. Rise=Y2-Y1 Run= X2-X1

Step 3: convert ratio.

Step 4: Find the coordinate point.

Find the coordinate point, P, that partitions segment RS.

Ex 1: RàS, ratio of 2:1

R(-3, 3) & S(6, -3)

Ex 2: AàB, ratio of 3:2

A(3, 4) & B(6, 10)

Ex 3: RàS, ratio of

R(-2, 4) & S(18, -6)

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Assignment

Find point P:

1. Given the points A(5, -1) and B(-5, 3), find the coordinates of the point P on directed line segment BA that partitions BA in the ratio 1:2.

2. Given the points A(-2, 1) and B(4, 5), find the coordinates of the point P on directed line segment BA that partitions BA in the ratio 3:6

3. Find the coordinates of P so that P partitions the segment AB in the ratio 5:1 if A(2, 4) and B(8, 10).

4. Find the coordinates of P so that P partitions the segment AB in the ratio 1 to 3 if A(-5, 4) and B(7, -4).