Line Segments, Distance and Midpoint

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Line Segments, Distance and Midpoint

• Partitioning a Segment

CC Standard G-GPE.6 Find the point on a directed
line segment between two given points that
partitions the segment in a given ratio.
At the end of this lesson, you should be able to
answer the following question How do you find
the point on a directed line segment that
partitions the segment in a given ratio?
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• Point P divides in the ratio 3 to 1.
• What does this mean?

3
-1
-7
Slope m

1
-1
7
-7
4
m
-4
5
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Slope Formula

• The slope of a line through the points
• (x1, y1) and (x2, y2) is as follows

m
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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).
Substitute 6 for y2, 3 for y1, 4 for x2, and
2 for x1.
Always reduce your fractions
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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.
Example 1
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?
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Partitioning a segment

• Label your points and
• Note since it is a directed segment, order
  does matter.

2. Convert the ratio into a percent (keep as a
fraction) ab Percent ratio
()
3. Find the rise and run for the segment (order
does matter) Rise
Run
4. To find the partitioning point x
coordinate x1 -coordinate run( in fraction
form) y - coordinate y1 -coordinate
rise( in fraction form)
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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.
1. Label your points. (note Since it is a
directed segment, order does matter, so A(x1, y1)
and B(x2, y2) ).
2. Convert the ratio into a percent
3. Find the rise and run for AB
4. The slope of AP must be the same as AB.
So, to find the coordinates of P, add 60 of the
run to the x-coordinate of A and add 60 of
the rise to the y-coordinate of A
How can you use the distance formula to check
that P partitions in the ratio of 3
to 2?
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Example 2 Find the coordinates of the point P
that lies along the directed segment from A(1, 1)
to B(7, 3) and partitions the segment in the
ratio of 1 to 4
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Example 3 Find the coordinates of point P that
lies along the directed line segment from M to N
and partitions the segment in the ratio of 3 to 2
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Essential question

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

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• Class assignment
• Partitioning a segment
• Page 210 7-8
• Worksheet Partitioning Segments