1.1 Line Segments, Distance and Midpoint 1.1d – Partitioning a Segment CC Standard G-GPE.6 Find...
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Transcript of 1.1 Line Segments, Distance and Midpoint 1.1d – Partitioning a Segment CC Standard G-GPE.6 Find...
1.1 Line Segments, Distance and Midpoint 1.1d – 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 in the ratio 3 to 1. 1. What does this mean?
AB
AP
= -1= -7
Slope = m = =
-1
-7
1
7
m = -4
5
Slope Formula
The 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
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.
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?
AB
1. Label your points. (note: Since it is a directed segment, order does matter, so A(x1, y1) and
B(x2, y2) ).
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:
Work sheet 1.1d – Partitioning a segment