Name———————————————————————— Lesson
1.3
Date —————————————
Practice A
For use with the lesson “Use Midpoint and Distance Formulas”
Line l bisects the segment. Find the indicated length.
1. Find AC if AB 5 6 cm.
A
B
E
G
H
J
6. Find ST if RT 5 109 in.
N
M
F
5. Find NP if NQ 5 31.8 cm.
L
D
K
C
3
4. Find LM if KM 5 24 ​ } ​in.
4
1
3. Find GJ if HJ 5 8 ​ } ​in.
4
2. Find DF if DE 5 17 cm.
P
R
S
T
}
7. Line CD bisects ​AB​ at point C. Find AC if AB 5 56 feet.
1
}
8. Point W bisects ​UV​ 
. Find UV if WV 5 11 ​ }8 ​inches.
9. Find XM.
10. Find MF.
x16
X
3x
M
5x
M
9x 2 13
M
K
4x 2 9
2x 1 5
G
M
H
14. Find PQ.
11x 2 21
L
F
13. Find LN.
6x 1 11
J
7x 2 6
E
Y
12. Find JK.
11. Find MH.
8x 1 15
M
N
10x 1 3
P
14x 2 13
M
Find the coordinates of the midpoint of the segment with the
given endpoints.
15. R(3, 1) and S(3, 7)
16. V(2, 4) and W(6, 6)
}
Lesson 1.3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
In each diagram, M is the midpoint of the segment. Find the
indicated length.
Use the given endpoint Y and midpoint M of YZ​
​  to find the coordinates of
the other endpoint Z.
17. Y(0, 5), M(3, 3)
18. Y(21, 23), M(5, 9)
Geometry
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4/28/11 3:08:22 PM
Name———————————————————————— Date —————————————
Practice A continued
Lesson
1.3
For use with the lesson “Use Midpoint and Distance Formulas”
Find the length of the segment. Round to the nearest tenth of a unit.
19.
y
20.
y
C(−3, 2)
B(6, 6)
1
x
1
A(2, 1)
1
D(4,−3)
x
1
Find the length of the segment. Then find the coordinate of the midpoint
of the segment.
21.
E
24 23 22 21
F
0
1
2
3
22.
4
G
H
28 26 24 22
0
2
4
6
8
25. Distances Your house and your school are 8.4 miles apart on the same straight road.
A baseball field is halfway between your house and your school, on the
same road.
a. Draw a sketch to represent this situation. Mark the locations of the house, school,
and field. How far is your house from the baseball field?
b. You walk at an average speed of 3 miles per hour. About how long would it take
you to walk from your house to the baseball field?
1-36
three soccer players. Player A kicks the ball
to Player B, who then kicks it to Player C.
How far did Player A kick the ball? How far
did Player B kick the ball? How far would
Player A have kicked the ball if she had kicked
it directly to Player C? Round all answers to the
nearest tenth of a yard.
y
20
Distance (yd)
Lesson 1.3
26. Soccer The diagram shows the position of
16 A(3, 18)
B(12, 14)
12
8
C(17, 6)
4
0
0
4
8
12
Distance (yd)
16
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
The endpoints of two segments are given. Find each segment length.
Tell whether the segments are congruent.
}
}
23.​
JK​:  J(1, 1), K(0, 5)
24.​PQ​:  P(4, 3), Q(21, 6)
}
}
​LM​:  L(1, 1), M(23, 2)​RS​:  R(2, 23), S(22, 0)
Geometry
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4/28/11 3:08:22 PM
Lesson 1.2 Use Segments and
Congruence, continued
Math and History Application
answers
1. A
B
2.
3.
5. Sample answer: No. The Distance Formula
was not needed if the segment connecting two
points was horizontal or vertical. Counting or
subtraction easily determined the answer.
6. Sample answer: Estimation and comparison
determined the distances to try first.
Technology Activity
A
B
A
B
1.
y AM 5 5.00
4.
A
C
BM 5 5.00
M : (21, 22)
2
x
1
M
B
A
B
D
}
Use a straight edge to draw ​CD​ . Let P be the point
}
}
​  intersect. n APC and n BPC
where ​CD​ and AB​
are right triangles.
Challenge Practice
1. By the Segment Addition Postulate, you know
2. They are congruent. 3. It is the average of
the x- and y-coordinates of points A and B.
4. The x-coordinate of the midpoint is the
average of the x-coordinates of the endpoints.
The y-coordinate of the midpoint is the average
of the y-coordinates of the endpoints.
AB 1 BC 5 AC and BC 1 CD 5 BD. Because
AB 5 CD, substitute CD for AB in AB 1 BC 5 AC
to obtain CD 1 BC 5 AC. You can then conclude
} } } } } }
​  > SU​
​  > TV​
​  > RT​
​ ;  ​QT​ > SV​
​  ; ​
AC 5 BD. 2. QS​
} }
QU​ > ​RV​ 
3. Not sufficient. Counterexample:
Practice Level A
A
15. (3, 4) 16. (4, 5) 17. (6, 1) 18. (11, 21)
D
F
B C
4. Not sufficient. Counterexample:
D
A F
B C
5. Sufficient. A
D F C B
AD 1 DF 1 FC 1 CB 5 AB
3
1
1. 12 cm 2. 34 cm 3. 16 ​ } ​in. 4. 12 ​ } ​in.
2
8
1
1
5. 15.9 cm 6. 54 ​ } ​in. 7. 28 ft 8. 22 ​ } ​in.
2
4
9. 9 10. 15 11. 19 12. 118 13. 222 14. 86
19. 6.4 20. 8.6 21. 4; 0 22. 10; 21
23. JK < 4.1, LM < 4.1; congruent
24. PQ < 5.8, RS 5 5; not congruent
25. a.
House
6. a. AF 5 GE 5 CH 5 HI 5 ID 5 4;
HD 5 IC 5 FB 5 DG 5 8; AC 5 CE 5 6;
4
​ 13  ​;  There are a
AB 5 CB 5 CD 5 DE 5 12 b. }
total of 13 segments in the diagram and 4 of those
segments have lengths greater than 8.
7. x 2 1 x 5 12; x 5 3; LM 5 9, MN 5 3
8. x 2 2 5x 5 50; x 5 10; LM 5 40, MN 5 10
7
49
175
9. 2x 1 9x 5 56; x 5 }
​ 2 ​; LM 5 }
​ 4  ​, MN 5 }
​  4    ​
2
Lesson 1.3 Use Midpoint and
Distance Formulas
; 4.2 mi
8.4 mi
Baseball
Field
School
b. about 1 h 24 min
26. about 9.8 yd; about 9.4 yd; about 18.4 yd
Practice Level B
1. 7 cm 2. 13.5 ft 3. 9 yd 4. 7.4 m 5. 24
1 
2
1
6. 26 7. 10 8. ​ 5, 2​ } ​  ​ 9. (2, 2) 10. (1, 4)
2
1 
2
1
11. ​ 22 ​ } ​, 210  ​ 12. (26, 4) 13. (3, 28)
2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
5. Answers will vary. 6. Repeat Exercises 124.
14. (1, 214) 15. (219, 23) 16. 3.2 17. 5.4
18. 4.5 19. 11.3 20. 9; 1.5 21. 7; 24.5
Teaching Guide
1–4. Answers will vary.
A4
Geometry
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4/28/11 2:35:33 PM