Midpoint Conjecture

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Midpoint Conjecture

• Objectives
• Discover formula for finding the midpoint of a
  segment.

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midpoint of a segment a point that divides
the segment into two equal halves (point right
in the middle of the segment)
10 ft.
10 ft.
P
P is the midpoint.
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You can calculate the midpoint on a coordinate
plane as long as you know the coordinates of the
endpoints!
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Look at this segment..can you guess the
coordinates of the midpoint?
Y
X
You will now learn the Midpoint Formularemember
your guess (above).
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Steps for Finding Midpoint
Y
X
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1. Label the endpoints as (x1,y1) and (x2,y2).
Y
(-4,2)
(4,2)
X
(x1,y1)
(x2,y2)
So.x1-4 y12 x24 y22
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We are going to find the average of the x y
coordinates using
Y
(4,2)
(-4,2)
X
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The Midpoint Formula
where (x1,y1) (x2,y2) are coordinates of
endpoint of segment.
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2. Plug x y values into the Midpoint
Formula
Y
(-4,2)
(4,2)
X
(x1,y1)
(x2,y2)
So.x1-4 y12 x24 y22
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Plug the numbers into the formula
x1-4 y12 x24 y22
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Plug the numbers into the formula
x1-4 y12 x24 y22
12
Plug the numbers into the formula
x1-4 y12 x24 y22
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Plug the numbers into the formula
x1-4 y12 x24 y22
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3. Simplify.


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The coordinates of the midpoint are
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Plot the calculated midpoint.was this what you
guessed earlier?
Y
X
This is the midpoint!!!
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Calculate the midpoint of the segment.
(2,3)
X
(12,-7)
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(x1,y1) (x2,y2).
(12,-7)
(2,3)
Plug the values into equation.
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(x1,y1) (x2,y2).
(12,-7)
(2,3)
Simplify.
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(x1,y1) (x2,y2).
(12,-7)
(2,3)
Simplify.
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Plot the calculated midpoint.
Y
(2,3)
X
(12,-7)
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Calculate the midpoint of the segment that has
endpoints at (-17,8) and (-1,11).