Partitioning a Segment

CC StandardG-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Objective: Students will be able to find the ratio of a partitioned line segment.

Inquiry Question: How do you find the point on a directed line segment that partitions the segment in a given ratio?

What does partition mean?To break apart into pieces!

Ratio: A comparison of 2 quantities.

Point P divides in the ratio 3 to 1. 1. What does this mean?

AB

2. Do you expect point P to be closer to A or closer to B? Why?

3. How does the slope of AP compare with the slope of the AB? Why?

Slope FormulaThe slope of a line through the points (x1, y1) and (x2, y2) is as follows:

yy22 –– yy11 xx22 –– xx11

m =

Ex.

Find the slope of the line that passes through (–2, –3) and (4, 6).

Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).

6 – (–3)4 – (–2)

Substitute 6 for y2, –3 for y1, 4 for x2, and –2 for x1.

=y2 – y1

x2 – x1

96= 3

2=

The slope of the line that passes through (–

2, –3) and (4, 6) is . 32

*** Always reduce your fractions****

Find the coordinate of point P that lies along the directed line segment from A(3, 4) to B(6, 10) and partitions the segment in the ratio of 3 to 2.

Directed Line Segment:Tells the direction in which from which point to start and end. In this case, from Point A to Point B So point A must be labeled A and B

What does that tell you about the distance AP and PB in relation to AB?

Example 1:

),( 11 yx ),( 22 yx

Partitioning a segment 1. Label your points and

Note: since it is a directed segment, order does matter.

),( 11 yx ),( 22 yx

3. Find the rise and run for the segment (order does matter)

Rise: Run: 12 xx 12 yy

4. To find the partitioning point:

x – coordinate: x1 -coordinate + run(% in fraction form)

y - coordinate: y1 -coordinate + rise(% in fraction form)

2. Convert the ratio into a percent (keep as a fraction) a:b

Percent ratio (%) ba

a

What is the ratio that segment AB is partitioned into a point by point P?

1. Focus on our y-intercepts.

2. AP: 4 - 8 = -4PB: 8-10 = -2 *Our ratio has to be positive, so we use absolute value {-4} = 4, and {-2} = 2

3. The ratio that segment AB is partitioned into a point by point P is 4:2 or 2:1

(5,8)

Example: What is the ratio that segment AB is partitioned into a point by point P?

B (4,6)

A (-5,1)

P (0,4)