Back to Lesson 11-7
Name
Name
11-6B
page 2
14.
(0, 6)
(6, 0)
(᎑6, 0)
y
center
(᎑3, 2)
SKILLS Objective B
In 1–4, the endpoints of a segment are given. Find the midpoint
of each segment.
x
x
1. (14, 12) and (6, 8)
(᎑3, ᎑1)
3. (m, n) and (m, 0)
(0, ᎑6)
x2 + y2 = 36
(x + 3)2 + (y - 2)2 = 9
y
15. a. Draw the circle with radius 4 and center at (–2, –3).
x
(4, 2)
17. (x – 8)2 + (y + 2)2 = 4
(8, –2)
a.
2
b.
a.
(–3.8, –2.2)
Answers vary. Sample:
(–3.8,
c. –0.5), (–2.1, –2.2)
Answers vary. Sample:
1.7
b.
(0, 0)
a.
(0, 8)
c.
542
(–19, 0)
2000, 8%
x
√
18 = 3 √
2
(0,c.8 + 3 √
2), (3 √
2, 8)
b.
1
Answers vary. Sample:
c. (–19, 1), (–18, 0)
y
(a + b, c)
(b, c)
Midpoints:
a+b _
a+b _
c
c
____
(____
2 , 2 ) and ( 2 , 2 )
Diagonals bisect each other?
x
yes
(0, 0)
(a, 0)
y
8. Isosceles trapezoid
Midpoints:
a–b _
b–a _
c
c
___
(___
2 , 2 ) and ( 2 , 2 )
Diagonals bisect each other?
A = (᎑b, c)
R = (b, c)
no
x
___
9. Consider AB where A = (0, 5) and
___B = (4, 3). Find the equation
of the perpendicular bisector of AB.
P = (᎑a, 0)
T = (a, 0)
y = 2x
Geometry
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Geometry
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Name
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Name
11-7B Lesson Master
Questions on SPUR Objectives
2. endpoints (0, 0) and (–10, –3)
3. endpoints (4, 9) and (19, 9)
4. endpoints (2.8, –13) and (–6.6, –4.2)
5. endpoints (7, –4) and (–1, 9)
(–1.5, 4.5)
(–5, –1.5)
(11.5, 9)
(–1.9, –8.6)
(3, 2.5)
___
7. CD
___
8. EF
Copyright © Wright Group/McGraw-Hill
___
9. FG
The diagonals bisect each other.
14. Use ABCD pictured at the right. Give an indirect argument to
prove that the diagonals of ABCD do not bisect___
each other.
___
Answers vary. Sample: If the diagonals AC
___ and BD
bisect each other, then
___AC coincides
___the midpoint of
with the midpoint___of BD. Midpoint of AC = (0, 0)
and midpoint of BD = (1, 0). Since (0, 0) ≠ (1, 0),
the diagonals of ABCD do not bisect each other.
y
A
E
5
D
᎑5
G
x
5
A = (0, 4)
D = (᎑4, 0)
(13, 4)
17.
PROPERTIES Objective H
___
y
6
(2.5, 2)
R
___
4
2
b. Write the equation of the perpendicular bisector of RS.
᎑4
᎑2
S
2
C = (0, ᎑4)
No
symmetry
lines
(–3.5, 0.25)
12. a. Find the midpoint of RS at the right.
x
B = (6, 0)
16. parallelogram
___
4
6
8
x
19. regular hexagon
No
symmetry
lines
18. equilateral triangle
20. rhombus
᎑2
Geometry
Geometry
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545
6/5/08
Geometry
SMP_TRGEO_A47-A90_EM_Vol_2.indd A71
x
In 15–20, draw the symmetry line(s), if any, for the figure.
15. rectangle
11. Find the midpoint of MZ, given that Z = (5, 1) and that M
is the midpoint of the segment with endpoints (14, –3)
and (28, 17).
544
Z = (7, 2)
y
___
SMP_LMGEO_C11_525-551.indd
Y = (10, 8)
REVIEW Lesson 6-1, Objective A
C
᎑5
B
F
10. Find the midpoint of PQ given that P = (–4, –4) and that Q
is the midpoint of the segment with endpoints (–12, 9)
and (6, 0).
y = 4.5x – 9.25
y
b. What can you conclude about the diagonals?
(–3, 2)
(0, 0)
(2.5, –0.5)
(–4, –5.5)
___
X = (0, 8)
8+2
0 + 7 ___
Answers vary.___
Sample: Midpoint of XZ = (___
2 , 2 ) = (3.5, 5);
2+8
–3 + 10 ___
midpoint of WY = (____
) = (3.5, 5). So (3.5, 5) is
2 , 2 ___
__
the midpoint of both XZ and WY.
W = (᎑3, 2)
In 6–9, refer to the coordinate grid at the right. Determine the
coordinates of the midpoint of the given segment.
6. AB
page 2
13. a. Prove that in parallelogram WXYZ, the midpoints
of the diagonals coincide.
__
SKILLS Objective B
1. endpoints (–8, 4) and (5, 5)
11-7B
See Student Edition pages 715–717 for objectives.
In 1–5, determine the coordinates of the midpoint of the
segment described.
544
2006, 69%
7. Parallelogram
(0, √
94), (– √
94, 0
b.
21. (x + 19)2 + y2 = 1
a.
y
PROPERTIES Objective H
In 7 and 8, find the midpoint of each diagonal and use the midpoints
to determine whether the diagonals bisect each other.
Answers vary. Sample:
20. x2 + (y – 8) 2 = 18
a.
√
94
b.
4 √
2
b. Find the radius of the circle.
Year
2
19. x 2 + y 2 = 94
(8, 3)
b. Explain what the midpoint represents.
18. (x + 3.8) + (y + 2.2) = 2.89
2
a. Find the center of the circle.
In 2003, 38.5% of internet users had broadband access.
Answers vary. Sample:
c.(4, 16), (–10, 2)
Answers vary. Sample:
c. (8, 0), (10, –2)
14
b.
____
(___
2 , 2 )
5. (4, 7) and (12, –1) are the endpoints of a diameter of a circle.
(2003, 38.5%)
(᎑2, ᎑3)
–5.5)
(3,
a+c b+d
2. (10, –3) and (–4, –8)
4. (a, b) and (c, d)
a. Find the midpoint of the segment on the graph.
In 16–21, an equation of a circle is given. a. Determine its center.
b. Determine its radius. c. Find two points on the circle.
a.
(10, 10)
(m, _2n )
6. In 2000, 8% of United States internet users had broadband access
at home. In 2006, 69% did. Assume the growth is linear.
b. Give two points on the circle.
Answers vary. Sample:
(2,c. –3),
(–2, 1)
What is an equation for this circle?
(x + 2)2 + (y + 3)2 = 16
16. (x – 4)2 + (y – 2)2 = 196
Questions on SPUR Objectives
See Student Edition pages 715–717 for objectives.
% of Internet Users
with Broadband
y
13.
Lesson Master
11-7A
1:26:19 PM
A71
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