Transcript 1.1 Line Segments, Distance and Midpoint

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?
Point P divides AB in the ratio 3 to 1.
1. What does this mean?
AP
= -1
= -7
1
-1
Slope = m =
=
7
-7
m=
-4
5
Slope Formula
The slope of a line through the points
(x1, y1) and (x2, y2) is as follows:
m=
y2 – y1
x2 – x1
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).
y2 – y1 6 – (–3)
Substitute 6 for y2, –3 for y1,
=
x2 – x1 4 – (–2)
4 for x2, and –2 for x1.
3
=9
=
6
2
The slope of the line that passes through
(–2, –3) and (4, 6) is 3.
2
*** Always reduce your fractions****
Example 1:
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 ( x1 , y1 ) and B ( x2 , y2 )
What does that tell you about the distance AP and PB in relation to AB?
Partitioning a segment
1. Label your points ( x1 , y1 ) and ( x2 , y2 )
Note: since it is a directed segment, order does matter.
2. Convert the ratio into a percent (keep as a fraction) a:b
Percent ratio (%)
a
a b
3. Find the rise and run for the segment (order does matter)
Rise: y2  y1
Run: x2  x1
4. To find the partitioning point:
x – coordinate: x1 -coordinate + run(% in fraction form)
y - coordinate:
y1 -coordinate + rise(% in fraction form)
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
ratio of 3 to 2?
AB in the
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
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
Essential question:
• How do you find the point on a directed
line segment that partitions the segment in
a given ratio?
• Class assignment:
Partitioning a segment:
Page 210: 7-8
Worksheet: Partitioning Segments