Partitioning of Line Segments 1-Variable And 2-Variable
Partitioning of Line Segments
Dec 31, 2015
Partitioning of Line Segments. 1-Variable And 2-Variable. Find a Point that Partitions a Segment in a Given Ratio a:b (1 variable). a: the first part of the ratio b: the second part of the ratio X 1 : first x value given X 2 : second x value given. Partition – 1 Variable. - PowerPoint PPT Presentation
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Partitioning of Line Segments
1-VariableAnd
2-Variable
2 1 1( )a
x x xa b
Find a Point that Partitions a Segment in a Given Ratio a:b
(1 variable)
2 1 1( )
ax x x
a b
a: the first part of the ratiob: the second part of the ratioX1: first x value givenX2: second x value given
Partition – 1 Variable
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.
a:b:
Partition – 1 Variable
A is at -6 and B is at 4.Find the point, T, so that T is A to B in a 2:3 ratio.
a:b:
Find a Point that Partitions a Segment in a Given Ratio a:b
2 Variables
2 1 1 2 1 1,a a
x x x y y ya b a b
2 1 1 2 1 1,a a
x x x y y ya b a b
a: the first part of the ratiob: the second part of the ratioX1: first x-value given y1: first y-value X2: second x-value given y2: second y-value
Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3:2.
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.
To find the coordinates of point P…
1 2 1 2 1 1,
a ax x x y y y
a b a b
3 33 3, 6 4
5 5
4.8, 7.6
3 36 3 3, 10 4 4
5 5
a:b:
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 : 1.
2 1 1 2 1 1, a a
x x x y y ya b a b
4 47 1, 1 3
5 5
6.6, 3.8
a:b:
4 48 1 1, 4 3 3
5 5
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.
2 1 1 2 1 1, a a
x x x y y ya b a b
3 36 2, 4 1
10 10
0.2, 2.2
a:b:
3 34 2 2, 5 1 1
10 10
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 : 4.
2 1 1 2 1 1, a a
x x x y y ya b a b
1 15 8, 2 0
5 5
7, 0.4
a:b:
1 13 8 8, 2 0 0
5 5
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.
2 1 1 2 1 1, a a
x x x y y ya b a b
3 38 2, 5 4
5 5
2.8, 1
a:b:
3 36 2 2, 1 4 4
5 5
1. (-1, 2), (3, -5) ratio 1:42. (5,5), (-6, 6) ratio 2:53) (0,0), (3, 4) ratio 2:1
CW/HW
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