Find a Point that Partitions a Segment in a Given Ratio
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Transcript Find a Point that Partitions a Segment in a Given Ratio
Warm up
A is at -1, and B is at -7.
Find the point, T, so that T partitions A to B
in a 2:1 ratio.
Warm up - 2
A is at -2, and B is at -7.
Find the point, T, so that T partitions A to B
in a 2:1 ratio.
a
(x2 x1)
x
1
a b
Review HW
Find a Point that Partitions a
Segment in a Given Ratio a:b
a
a
a b x2 x1 x1, a b y2 y1 y1
Find the coordinates of P along the directed line
segment AB so that the ratio of AP to PB is 3 to 2.
In order to divide
the segment in the
ratio of 3 to 2, think
of dividing the
segment into 3 + 2
or 5 congruent
pieces.
A(3, 4), B(6, 10); 3 to 2.
3
6
AB has a rise of 6.
AB has a run of 3.
A(3, 4), B(6, 10); 3 to 2.
To find the coordinates
of point P…
a
a
a b run x1, a b rise y1
3
3
5 3 3, 5 6 4
4.8, 7.6
3
6
Example 1: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(1, 3), B(8, 4); 4 to 1.
a
a
x
x
x
,
y
y
y
1
1
a b 2 1 1 a b 2
4
4
5 7 1, 5 1 3
6.6, 3.8
Example 2: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(-2, 1), B(4, 5); 3 to 7.
a
a
x
x
x
,
y
y
y
1
1
a b 2 1 1 a b 2
3
3
10 6 2, 10 4 1
0.2, 2.2
Example 3: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(8, 0), B(3, -2); 1 to 4.
a
a
x
x
x
,
y
y
y
1
1
a b 2 1 1 a b 2
1
1
5 5 8, 5 2 0
7,
0.4
Example 4: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2.
a
a
x
x
x
,
y
y
y
1
1
a b 2 1 1 a b 2
3
3
5 8 2, 5 5 4
2.8,
1
CW/HW
New York Task