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# Partitioning A Segment

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by

## Lori Winkleman

on 8 October 2017

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#### Transcript of Partitioning A Segment

Using Slope to Partition A Segment
Ratio
A ratio is a comparison of two quantities.
Find the coordinates of the point P that lies along the directed line segment from
A
(3, 4) to
B
(6, 10) and partitions the segment in the ratio 3 to 2.
The Challenge
Can you find the point on a line segment that partitions the segment into a given ratio?
Step 2: Determine Delta of x and y
Step 1: Convert the Ratio
The ratio of
a
to
b
can be expressed as:
What is the ratio of...
Stars to hearts?
Hearts to stars?
Stars to total shapes?
Hearts to total shapes?
In a coordinate plane, slope is the ratio of
rise
to
run
.
Slope of a Straight Line
a
:
b

or

a
b
Step 3: Determine Increase in x and y
Step 4: Calculate the Location of Point P
To determine how much to increase
x
and
y
, the delta of
x
and the delta of
y
must each be multiplied by the converted ratio.
The last step is to add the amount of change in
x
and
y
determined in Step 3 to the original
x
and
y
value of the first endpoint.
Step 1:
Convert the ratio
Step 2:
Determine delta of
x
and
y
Step 3:
Determine the increase in
x
and
y

Step 4:
Calculate the new point
Steps for Partitioning a Segment
The Problem
The ratio of 3 to 2 must be first converted into a percent
numerator
numerator + denominator
3
3 + 2
3
5
=
=
Remember, delta is the change or difference in values. You will need to find the delta of
x
and the delta of
y
separately.
x
= 6 - 3 = 3
A directed line segment is a line segment that has a direction associated with it. It moves from one endpoint to the other.
Original Coordinates:
A
(3, 4) to
B
(6, 10)
Original Coordinates:
A
(3, 4) to
B
(6, 10)
y
= 10 - 4 = 6
The triangle is the symbol used to represent delta.
y

Increase in
y
:
3
5
converted ratio
6
=
18
5
= 3.6
x

Increase in
x
:
3
5
converted ratio
3
=
9
5
= 1.8
x
value for Point P
3 + 1.8 = 4.8
Starting
x
value
Increase in
x
+
y
value for Point P
4 + 3.6 = 7.6
Starting
y
value
Increase in
y
+
Coordinates of Point P
The directed line segment from
A
(3, 4) to
B
(6, 10) is partitioned at the ratio of 3 to 2 at point
P
(4.8, 7.6)
.
Full transcript