Name————————————————————————
Date —————————————
Practice C
Lesson
1.3
For use with the lesson “Use Midpoint and Distance Formulas”
Find the indicated length.
}
1. Line JK bisects LM at point J. Find JM if L J 5 23 centimeters.
5 } 2. Line WX bisects YZ at point W. Find YZ if WZ 5 9 } inches. 8 7 } . Find GH if GF 5 14 } feet. 3. Point F bisects GH 12
}
4. Point R bisects ST. Find RT if ST 5 16.9 meters.
In the diagram, M is the midpoint of the segment. Find the indicated length. 5. Find MQ.
6. Find UV.
4x 2 1 P
12x 2 17 M
7. Find DE.
21x 2 13 U
10x 1 31 M
V
5x 2 6 D
2x 1 5 M
E
Find the coordinates of the midpoint of the segment with the given endpoints.
8. A(6, 23) and B(10, 5)
9. M(14, 7) and N(29, 1) 11. C(25, 217) and D(218, 12) }
Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S.
12. R(8, 0), M(4, 25)
13. R(7, 217), M(22, 3)
14. R(26, 29), M(8, 25.5)
15. R(11, 216), M(23.5, 29.5)
Find the length of the segment. Round to the nearest tenth of a unit. 16.
y
17.
y
G(− 3, 2)
B (7, 4)
1 1
A (1, 2)
x
1 x
1
H (3, −3)
18.
2
y
19.
Lesson 1.3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
10. Y(213, 8) and Z(2, 210)
y
N(−1, 2) 1
S (− 2, 0) x
1
T (5, −4)
1 x
M (− 4, −4)
Geometry Chapter Resource Book
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1-39
4/28/11 3:10:10 PM
Name———————————————————————— Lesson
1.3
Date —————————————
Practice C continued
For use with the lesson “Use Midpoint and Distance Formulas”
Find the length of the segment. Then find the coordinate of the midpoint of the segment. 20.
J 220 216 212 28
K 24
0
21.
4
P 240 230 220 210
0
10
20
The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent. } } 22. AB: A(7, 2), B(0, 23) 23. RS: R(5, 6), S(11, 22) } } CD: C(24, 12), D(21, 4) TU: T(27, 9), U(3, 9) } } 24. KL: K(210, 8), L(2, 7) 25. OP: O(26, 12), P(0, 7) } } MN: M(14, 24), N(5, 4) QR: Q(8, 25), R(12, 2)
Buffalo, NY
(5075, 2326)
Omaha, NE
(6687, 4595)
Chicago, IL
(5986, 3426)
Providence, RI
(4550, 1219)
Dallas, TX
(8436, 4034)
San Diego, CA
(9468, 7629)
Miami, FL
(8351, 527)
Seattle, WA
(6336, 8896)
26. Buffalo and Miami
27. Chicago and San Diego
28. Dallas and Seattle
29. Omaha and Providence
In Exercises 30–32, use the map. 30. Find the distance between each pair of towns.
y
31. Which two towns are closest together?
Which two towns are farthest apart?
Lesson 1.3
32. The map is being used to plan a 36-mile bicycle
1-40
race. Which of the following plans is the best route for the race? Explain. A. Dunkirk to Clearfield to Allentown to Dunkirk B. Dunkirk to Clearfield to Lake City to Allentown to Dunkirk C. Dunkirk to Lake City to Clearfield to Dunkirk D. Dunkirk to Lake City to Allentown to Dunkirk
Distance (mi)
Round to the nearest tenth of a mile.
Lake City (3, 8) Clearfield (− 1, 6) 2
Dunkirk (− 5, −4)
Allentown (7, 0) 2
Distance (mi)
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
In Exercises 26–29, find the distance between the two cities using the information in the table. Each data point is from a coordinate system used for calculating long-distance telephone rates. Round your answer to the nearest whole unit.
Geometry Chapter Resource Book
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4/28/11 3:10:10 PM
Lesson 1.3 Use Midpoint and Distance Formulas, continued }
}
22. AB 5 Ï 13 ; CD 5 Ï 13 ; congruent }
24. KL 5 Ï 85 ; MN 5 9; not congruent 25. OP 5 3; QR 5 5; not congruent 26. a. House
Movie Theater
Mall
4.8 mi b. 1.5 h
9.6 miles
27. Dunkirk to Clearfield 5 10.2 mi; Dunkirk to Lake City 5 8.6 mi; Dunkirk to Allentown 5 4.1 mi; Clearfield to Lake City 5 7.1 mi; Clearfield to Allentown 5 9.2 mi; Lake City to Allentown 5 5 mi 28. Dunkirk and Allentown; Dunkirk and Clearfield 29. Choice C; the total distance of the path is closest to 26 mi.
Practice Level C 1 1 1. 23 cm 2. 19 } in. 3. 29 } ft 4. 8.45 m 4 6 2 5. 7 6. 142 7. 24 } 8. (8, 1) 9. (2.5, 4) 3 10. (25.5, 21) 11. (211.5, 22.5) 12. (0, 210) 13. (211, 23) 14. (22, 22)
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
15. (218, 23) 16. 6.3 17. 7.8 18. 8.1 19. 6.7 20. 16; 26 21. 45; 27.5 22. AB < 8.6, CD < 8.5; not congruent 23. RS 5 10, TU 5 10; congruent 24. KL < 12.0, MN < 12.0; congruent 25. OP < 7.8, QR < 8.1; not congruent 26. 3737 units 27. 5458 units 28. 5296 units 29. 3996 units 30. Dunkirk to Clearfield: 10.8 mi; Dunkirk to Lake City: 14.4 mi; Dunkirk to Allentown: 12.6 mi; Clearfield to Lake City: 4.5 mi; Clearfield to Allentown: 10 mi; Lake City to Allentown: 8.9 mi 31. Clearfield and Lake City; Dunkirk and Lake City 32. D; The total distance of this route (35.9 mi) is closest to 36 miles.
Study Guide
1. a. 14 mi b. about 11.4 mi c. about 2.6 mi 2. a. A
B
C
b. 1125 ft 3. Y(2, 21);
Use the points S and T to find point W. Then use the midpoint formula with point W and point X to find the coordinates of point Y. 4. 2 5. EDC, DCF, CFE, FED; The intersection of planes ABC @ ##$ . 6. a. 82 mi b. about 1.5 h and BGF is BC c. Yes; The total time of the trip is 1.5 1 3(1.75) 5 6.75 hours which is less than 8 hours. Challenge Practice 3x1 1 x2 3y1 1 y2 x1 1 x2 y1 1 y2 1. } 4 , } , } 2 , } 2 , 4 x1 1 3x2 y1 1 3y2 7 5 3 7 } 4 , } 4 2. a. } 4 , 2 }4 , } 2 , 2 }2 , 5 3 9 3 3 1 13 4 , 2 }4 b. 2} 2 , 2 }4 , 21, 2 }2 , 2} 2 , 2 }4 }
1
2 1
1
1
2
2
2
2 1 2 1
1
1
2 1
2
2
3. Sample answer: To determine whether three points A, B, and C in a coordinate plane are collinear, find AB, BC, and AC. By the Segment Addition Postulate, if AB 1 BC 5 AC, then B is between A and C, and when one point is between two other points, then the three points are collinear. 4. Collinear 5. Not collinear 6. Not collinear
1
2
} 13 7. Collinear 8. AB 5 Ï 29 , M 5 5, 3, } 2
1 1
2
} 15 9. AB 5 Ï 13 , M 5 3, 1, } 2 } 9 9 13 10. AB 5 Ï 19 , M 5 2} 2 , }2 , } 2
1
2
5 11. AB 5 17, M 5 } 2 , 2, 6
2
12. a. (15, 22.5), (45, 22.5) b. 30 units
Lesson 1.4 Measure and Classify Angles Teaching Guide 1. piece 1; Sample answer: no, that piece is so
1. 20 cm 2. 50 mm 3. 74 in. 4. 15 cm
2
3 5. (2, 4) 6. 1 4, } 2 7. (8, 3) 8. (3, 2) 5 5 9. (1, 1) 10. } , 2 } 11. 7.2 12. 6.4 2 2
1
large that there wouldn’t be room for seven of the other pieces within the circle.
2
Geometry Chapter Resource Book
CS10_CC_G_MECR710761_C1AK.indd 5
answers
23. RS 5 5; TU 5 5; congruent
Problem Solving Workshop: Mixed Problem Solving
A5
4/28/11 2:35:33 PM
