Name: Date: 1.4.4 Slope and Directed Line Segments A directed line segment AB is a segment that represents moving from Point A to Point B. The components of directed line segment ABshown below are (x2 – x1, y2 – y1).
(Basically, you subtract the 2nd letter from the 1st letter)
1) Find the components of PQ

A possible “route” from P to Q is 4 units right and 2 units up.
2a) Find the components of QP

b) What’s a possible route from Q to P?
2
Find the components of each:
A(3, -6), B(x, y), C(-6, -2), D(5, -1), E(3, 10)
3) DA 4) BC
5) CB 6) DE
7) EB 8) CD
9) DB 10) AE
3
11) Fill in this chart with the other ways to write ratios:
3 to 4

1:2

5
3

4:3

7 to 1

12) If somebody tells you to place the point P so that it “partitions the line segment ABusing the ratio 3:4,” that means that APwould be 3 units long while PBwould be 4 units long. Draw this situation below.
13) Based on your drawing from #12, which of the following are true?
a.) 74AB = PB b.) 73AB = AP
c.) 34AP = PB d.) 43PB= AP
e.) 4AP= 3 PB f.) 4AB= 7 PB
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* You’ll only have to come up with one of these statements on your own. But I thought I’d show you that there are many ways to set it up.
14) Place the point P so that it “partitions the line segment ABusing the ratio32. Draw this AND come up with a statement that compares sizes.
Okay! We’re finally ready to do a real problem.
15) Given the points A(–1, 2) and B(7, 8), find the coordinates of the point P on directed line segment ABthat partitions ABin the ratio31. In order to divide the segment in the ratio 1 to 3, think of dividing or partitioning, the segment into 1 + 3, or 4 congruent pieces. Point P is ¼ of the way from point A to point B. Find the rise and run from A to B. slope of AB = 68=��������
������=��2−��1
��2−��1.
To find P, add ¼ of the run to the x-coordinate of A, and add ¼ of the rise to the y-coordinate of A. Notice that components of directed line segment line segment ABshown below are (x2 – x1, y2 – y1) = (run, rise) and we are taking 1/4th of each component and adding it to the starting point’s x-coordinate and y-coordinate, respectively.

Find P and verify its coordinates are the same as above.
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Multiple Choice Practice
16) Given the points P(2, –1) and Q(–9, –6), what are the coordinates of the point on directed line segment PQ that partitions PQ in the ratio 3:2?
−, 2
5
5 D. ⎟⎠⎞

−
8
⎜⎝⎛−

−, 4
23 C. ⎟⎠⎞ ⎜⎝⎛−

23 B. ⎟⎠⎞

A. ⎟⎠⎞
⎜⎝⎛ −
5
−, 3 ⎜⎝⎛ − 5
3
,
3
3

Practice Questions:
17) Find the coordinates of P so that P partitions the segment ABin the ratio 5:1 if A(2, 4) and B(8, 10)
18) Find the coordinates of P so that P partitions the segment ABin the ratio 1 to 3 if A(-5, 4) and B(7, -4)
19) Find the coordinates of P so that P partitions the segment ABin the ratio 3:4 if A(-9, -9) and B(5, -2)
20) Find the coordinates of P so that P partitions the segment ABin the ratio52if A(-8, -2) and B(6, 19)