Fundamentals: Midpoints!
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Midpoint of a Segment
1. How many midpoints does a given segment have?
2. How many midpoints does a given line have?
3. Given the number line answer the following questions:
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a. What is the midpoint of AB ?
b. What is the coordinate of the midpoint of QB ?
c.! What is the coordinate of the midpoint of WA ?
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d.! The coordinate of the midpoint of AR is –5. What is the coordinate of point R?
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e.! The coordinate of the midpoint of ST is 7. What is the coordinate of point T?
Fundamentals: Midpoints!
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4. M is the midpoint of AB. AM = 4x+7 and BM = 31.
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A
M
Find x.
B
5. XY = 3x+4, YZ = 4x and XZ = 32. Find x, XY and YZ.
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X
Y
Z
6. Y is the midpoint of XZ. XY = 4b+17 and YZ = 10b+5. Find XY, YZ and XZ.
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X
Y
Z
Fundamentals: Midpoints!
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7. AB = 3x-7, BC = 2x+5, CD = 6 and AD = 34. Find x, BC and BD.
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8.
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A
B
C
M
Find x.
4
x − 4 and BM = x+5.
3
Find x.
B
9. M is the midpoint of AB. AM =
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1
x + 4 and BM = 10.
2
M is the midpoint of AB. AM =
A
A
M
D
B
Fundamentals: Midpoints!
10.
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AM =
A
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1
x + 6, BM = 2x-2 and AB = 48. Find x, AM and BM.
2
M
B
11. (SAT Problem)
5
1
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If n = 60 , then n = ?
6
6
12.! For what value of x is Q the midpoint of PR?
P
Q
x 2 +2x
R
x 2 +8
48
Fundamentals: Midpoints!
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13. (SAT Problem)
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If AB = BC, then what is the x-coordinate of point B?
y
(1, 4)
(x, y)
A
B
(11, 4)
C
x
14. MCAS 2003 Retest)
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Four distinct points are shown on the number line below:
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W
X
Y
Z
How many distinct line segments have two of these points as endpoints?
a. 3!
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b. 6! !
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c. 9! !
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d. 12
The Midpoint Formula
Draw the segment and find the midpoint:
15. (0, 5) and (6, 1)! !
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16. (–2, –4) and (–8, 0)
Midpoint: __________!
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Midpoint: __________
Fundamentals: Midpoints!
17. (4, 4) and (6, –6)! !
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Midpoint: __________!
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18. (1, 8) and (3, 8)
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Midpoint: __________
19. Find the value of a if the midpoint of the segment with endpoints at (a, 2) and
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(3a, –4) is at (–6, –1)
20.
M is the midpoint of AB . Find the coordinates of B, given A(2, –4) and
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9⎞
⎛7
M⎜ , − ⎟ .
⎝6
5⎠
21. AB has endpoints A(k, k) and B(7, p). The midpoint of AB is (3, –4).
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Solve for k and p.