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Transcript

Using Slope to Partition A Segment

Step 1: Convert the Ratio

The ratio of 3 to 2 must be first converted into a percent

3

numerator

=

3 + 2

numerator + denominator

The Challenge

The Problem

Step 2: Determine Delta of x and y

Remember, delta is the change or difference in values. You will need to find the delta of x and the delta of y separately.

A directed line segment is a line segment that has a direction associated with it. It moves from one endpoint to the other.

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.

Can you find the point on a line segment that partitions the segment into a given ratio?

The triangle is the symbol used to represent delta.

Steps for Partitioning a Segment

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

Original Coordinates: A(3, 4) to B(6, 10)

x = 6 - 3 = 3

Original Coordinates: A(3, 4) to B(6, 10)

What is the ratio of...

Increase in y:

Increase in x:

y

converted ratio

x

converted ratio

Step 3: Determine Increase in x and y

18

3

6

=

= 3.6

9

3

5

3

=

= 1.8

Ratio

5

Hearts to stars?

Stars to hearts?

Stars to total shapes?

Hearts to total shapes?

Slope of a Straight Line

In a coordinate plane, slope is the ratio of rise to run.

Step 4: Calculate the Location of Point P

A ratio is a comparison of two quantities.

The ratio of a to b can be expressed as:

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.

a

a:b or

b

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).

x value for Point P

Starting

x value

Increase in x

+

3 + 1.8 = 4.8

3

5

y value for Point P

Starting

y value

Increase in y

+

4 + 3.6 = 7.6

y = 10 - 4 = 6

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