Question

Explain what a directed line segment is and describe how you would find the coordinates of point P along a directed line segment AB that partitions AB so that the ratio of AP to PB is 3:1.

Answer 1

Answer: see below

Explanation:

In order to partition line segment AB so that AP and PB have a ratio of 3 : 1

1) Find the x- and y-lengths of the segment AB.

2) Divide the x- and y-lengths by (3 + 1) to find the length of one section.

3) Add 3 times those lengths to point A to find point P ...or...

Subtract 1 times those lengths from point B to find point P.

For example: Consider A = (0, 0) and B = (4, 8)

1) The length from A to B is

x = 4-0 = 4

y = 8-0 = 8

2) Divide those by (3 + 1):

x = 4/4 = 1

y = 8/4 = 2

3) Add 3 times those values to A to find point P:

x = 0 + 3(1) = 3

y = 0+3(2) = 6

--> P = (3, 6)

Note: We could have also subtracted 1 from the x-value of B and 2 from the y-value of B to find that point P = (4-1, 8-2) = (3, 6)

Now we know that the distance from point A to point P is 3 times the distance from point P to point B.