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Midpoint Formula
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Write the equation of the line:1. Parallel (∥) to 8x – 2y = 6
and goes through (5, -2) in Standard form
Warm up
MidpointGiven 2 ordered pairs,
it’s theAVG of the x’s and
AVG of the y’s.
Midpoint Formula
1 2 1 2,2 2
x x y y
Find the midpoint.
1. (3, 7) and (-2, 4)
2. (5, -2) and (6, 14)
(.5, 5.5)
(5.5, 6)
Find the midpoint.
3. (3, -9) and (14, 16)
4. (12, 17) and (-7, 9)
(8.5, 3.5)
(2.5, 13)
Find the midpoint.5.
(2, 3)
Find the midpoint.6.
(1.5, 4)
Given the midpt and one endpt, find the other endpt.
7. Midpt (3, -6) Endpt (7, -3)
(-1, -9)
Given the midpt and one endpt, find the other endpt.
8. Midpt (-1, 2) Endpt (3, 0)
(-5, 4)
Given the midpt and one endpt, find the other endpt.
9. Midpt (-4, 6) Endpt (2, 1)
(-10, 11)
Partition Line Segments(1 Dimension)
2 1 1( )
ax x xa b
Partition – 1 Dimension
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.
Partition – 1 Dimension
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.
Find a Point that Partitions a Segment in a
Given Ratio a:b
2 1 1 2 1 1,a ax x x y y ya b a b
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.
AB has a rise of 6.
6
AB has a run of 3.
3
A(3, 4), B(6, 10); 3 to 2.
To find the coordinates of point P…
6
3
1 1, a arun x rise ya b a b
3 33 3, 6 45 5
4.8, 7.6
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.
2 1 1 2 1 1, a ax x x y y ya b a b
4 47 1, 1 35 5
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.
2 1 1 2 1 1, a ax x x y y ya b a b
3 36 2, 4 110 10
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.
2 1 1 2 1 1, a ax x x y y ya b a b
1 15 8, 2 05 5
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.
2 1 1 2 1 1, a ax x x y y ya b a b
3 38 2, 5 45 5
2.8, 1
HomeworkPartitioning Segments Worksheet