Lesson 11.1 Skills Practice
Name_________________________________________________________ Date__________________________
Four Quadrants Extending the Coordinate Plane
Vocabulary Define each term in your own words. 1. quadrant
2. Cartesian coordinate plane
Problem Set Plot the point represented by each coordinate pair in the coordinate plane. Determine in which quadrant the point lies or on which axis. 1. A (5, 8)
Quadrant I
y
2. B (22, 26)
6
3. C (24, 3)
4 2
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4. D (0, 28) 5. E (1, 3) 6. F (3, 22) 7. G (27, 29)
A
8
–8
–6
–4
–2 0 –2
2
4
6
8 x
–4 –6 –8
8. H (5, 26) 9. I (9, 0)
10. J (21, 7)
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Lesson 11.1 Skills Practice
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Write the coordinate pair for each point. Determine in which quadrant the point lies or on which axis. 11. Point A (2, 5) Quadrant I
F
12. Point B
y 8 6
13. Point C
4 C
14. Point D
H
A D
2
I
15. Point E
–8
–6
16. Point F
–2 0 –2
2
4
6
8 x
E
–4
J
17. Point G
–4
B –6
G
–8
18. Point H 19. Point I 20. Point J
Points A and B are labeled on each coordinate plane. Identify the ordered pair associated with each point. Write an absolute value equation to calculate the distance between point A and point B. 21.
22. A A
B
Point A (4, 8) Point B (4, 22) |8| 1 |22| 5 10
670 • Chapter 11 Skills Practice
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B
Lesson 11.1 Skills Practice
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Name_________________________________________________________ Date__________________________ 23.
24.
A
A
B
25.
B
26.
A A B
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B
Chapter 11 Skills Practice • 671
Lesson 11.1 Skills Practice
27.
page 4
28.
A
B
A
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B
672 • Chapter 11 Skills Practice
Lesson 11.2 Skills Practice Name_________________________________________________________ Date__________________________
Geometry and Graphs Graphing Geometric Figures
Problem Set Plot and label the points to create the figure or figures described. 1. The points A(2, 0) and B(2, 4) are plotted on the coordinate
y
plane. Plot and label points C, D, E, and F so that two
8 6 (22,4)E 4
squares, ABCD and ABEF, are formed. Draw the squares.
C(6,4)
B(2,4)
2 –8
–6
–4
D(6,0)
A(2,0)
(22,0)F –2 0 –2
2
4
6
8
x
6
8
x
–4 –6 –8
2. The points A(22, 2) and B(2, 2) are plotted on the
y
coordinate plane. Plot and label points C, D, E, and F so
8
that two squares, ABCD and ABEF, are formed.
6
Draw the squares.
4
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A(−2,2) –8
–6
–4
2
–2 0 –2
B(2,2) 2
4
–4 –6 –8
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Lesson 11.2 Skills Practice
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y
3. The points A(24, 2) and B(24, 7) are plotted on the B(−4,7)
coordinate plane. Plot and label points C, D,
8
E, and F so that two squares, ABCD and ABEF, are
6
formed. Draw the squares.
4 2
A(−4,2) –8
–6
–4
–2 0 –2
2
4
6
8
x
–4 –6 –8
4. The points A(22, 24) and B(3, 24) are plotted on
y
the coordinate plane. Plot and label points C, D,
8
E, and F so that two squares, ABCD and ABEF,
6
are formed. Draw the squares.
4 2 C(3,1) –8
–6
–4
–2 0 –2
2
–4
A(−2,−4)
4
6
8 x
B(3,−4)
–6 –8
y
5. Line segment AB is plotted on the coordinate
8
plane. Plot and label points C and D so that
6 A(−3,4)
Draw the parallelogram.
B(5,4)
4 2
–8
–6
–4
–2 0 –2 –4 –6 –8
674 • Chapter 11 Skills Practice
2
4
6
8
x
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parallelogram ABCD with a height of 6 units is formed.
Lesson 11.2 Skills Practice
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Name_________________________________________________________ Date__________________________ 6. Line segment AB is plotted on the coordinate
y
plane. Plot and label points C and D so that
8 A(−2,6)
parallelogram ABCD with a height of 2 units is formed. Draw the parallelogram.
B(3,6)
6 4 2
–8
–6
–4
–2 0 –2
2
4
6
8
x
–4 –6 –8
7. Line segment AB is plotted on the coordinate plane. Plot and label points C and D so that trapezoid ABCD with a height of 4 units is formed. Draw the
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trapezoid.
A
B
8. Line segment AB is plotted on the coordinate plane. Plot and label points C and D so that trapezoid ABCD with a height of 3 units is formed. Draw the trapezoid.
B
A
Chapter 11 Skills Practice • 675
Lesson 11.2 Skills Practice
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Graph the points on each coordinate plane. Connect the points with line segments and identify the resulting figure. 9.
x
y
1
21
0
25
23
27
24
22
The figure is a quadrilateral.
x
y
1
3
1
7
23
5
23
1
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10.
676 • Chapter 11 Skills Practice
Lesson 11.2 Skills Practice
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Name_________________________________________________________ Date__________________________ 11.
y
4
3
7
3
7
25
4
25
x
y
22
2
24
7
26
7
28
2
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12.
x
Chapter 11 Skills Practice • 677
Lesson 11.2 Skills Practice
13.
y
22
23
28
23
25
27
x
y
3
2
5
2
6
5
4
7
2
5
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14.
x
page 6
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Lesson 11.2 Skills Practice
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Name_________________________________________________________ Date__________________________ Plot and label the points to create each figure described. 15. The points A(23, 21) and B(5, 24) are endpoints of one diagonal of a rectangle. Plot and label points C and D so that the rectangle ACBD is formed. Draw the rectangle.
A
D
C
B
16. The points A(22, 5) and B(26, 23) are endpoints of one diagonal of a rectangle. Plot and label A
points C and D so that the rectangle ACBD is formed. Draw the rectangle.
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B
Chapter 11 Skills Practice • 679
Lesson 11.2 Skills Practice
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17. The points A(3, 3) and B(3, 23) are endpoints of one
y
diagonal of a square. Plot and label points C and D
8
so that square ACBD is formed. Draw the square.
6 4
A(3,3)
2 –8
–6
–4
–2 0 –2 –4
2
4
6
8
x
6
8
x
B(3,−3)
–6 –8
18. The points A(27, 5) and B(1, 5) are endpoints of one
y 8
diagonal of a square. Plot and label points C and D so that square ACBD is formed. Draw the square.
A(−7,5)
6
B(1,5)
4 2 –8
–6
–4
–2 0 –2
2
4
–4 –6 –8
19. Plot and identify 5 points that are the vertices of a
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pentagon. Draw the pentagon.
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Lesson 11.2 Skills Practice
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Name_________________________________________________________ Date__________________________ 20. Plot and identify 4 points that are the vertices of
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a parallelogram. Draw the parallelogram.
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682 • Chapter 11 Skills Practice
Lesson 11.3 Skills Practice Name_________________________________________________________ Date__________________________
Water, Water Everywhere Solving Problems with Multiple Representations
Problem Set Complete each table. 1. A free diver is diving at a constant rate of 1.2 feet per second. Complete the table to show the diver’s depth, d, after t seconds. Time, t (in seconds)
Depth, d (in feet)
30
236
60
90
120
2. An airplane is taking off and climbing at a constant rate of 1400 feet per minute. Complete the table to show the airplane’s altitude, a, after t minutes.
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Time, t (in minutes)
Altitude, a (in feet)
1
1.5
2
2.5
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Lesson 11.3 Skills Practice
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3. A mountain climber is ascending a challenging section of a mountain at a rate of 3 feet per minute. Complete the table to show the height that the climber ascends, h, after t minutes. Time, t (in minutes) 2
Height, h (in feet)
4 6 8
4. A helium balloon is rising at a constant rate of 300 feet per minute. Complete the table to show the balloon’s altitude, a, after t minutes. Time, t (in minutes) 0.25
Altitude, a (in feet)
0.5 1 1.5
5. A backyard pool is being filled with water at a constant rate of 5 gallons per minute. Complete the
Time, t (in minutes)
Volume, v (in gallons)
30 60 90 120
684 • Chapter 11 Skills Practice
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table to show the volume of water added to the pool, v, after t minutes.
Lesson 11.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 6. A submarine is diving at a constant rate of 8 feet per second. Complete the table to show the submarine’s depth, d, after t seconds. Time, t (in seconds)
Depth, d (in feet)
15 30 45 60
Write an equation that represents each situation. 7. A free diver is diving at a constant rate of 0.9 feet per second. t 5 time in seconds d 5 depth in feet d 520.9t
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8. An airplane is taking off and climbing at a constant rate of 2000 feet per minute.
9. A mountain climber is ascending a challenging section of a mountain at a rate of 2 feet per minute.
10. A helium balloon is rising at a constant rate of 400 feet per minute.
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Lesson 11.3 Skills Practice
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11. A backyard pool is being filled with water at a constant rate of 4.5 gallons per minute.
12. A submarine is diving at a constant rate of 12 feet per second.
Graph the equation that represents each situation. 13. A free diver is diving at a constant rate of
Time, t (in seconds)
0.75 feet per second.
0
t 5 time in seconds
–20 –40
d 5 depth in feet
40
60
80 100 120 140 160 180 200
d = –0.75t
–60 Depth, d (in feet)
d 5 20.75t
20
–80 –100 –120 –140 –160 –180 –200
rate of 1500 feet per minute.
686 • Chapter 11 Skills Practice
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14. An airplane is taking off and climbing at a constant
Lesson 11.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 15. A mountain climber is ascending a mountain at a rate of 5 feet per minute.
16. A helium balloon is rising at a constant rate of
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200 feet per minute.
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Lesson 11.3 Skills Practice
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17. A backyard pool is being filled with water at a constant rate of 4 gallons per minute.
18. A submarine is diving at a constant rate of
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10 feet per second.
688 • Chapter 11 Skills Practice
Lesson 11.4 Skills Practice Name_________________________________________________________ Date__________________________
Every Graph Tells a Story! Interpreting Graphs
Problem Set Tell a story to describe each graph.
Heart Rate (beats per minute)
1.
Time Spent Exercising (in minutes)
Answers may vary. The person’s heart rate increased as she warmed up and began to exercise. Then, it leveled off as she exercised at a steady pace for a while. Her heart rate began to fall back to normal as she slowed down and cooled off at the end.
Temperature of Tea (°F)
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2.
Time Spent Cooling (in minutes)
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Lesson 11.4 Skills Practice
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Water Level of Bird Bath (in inches)
3.
Time (in days)
Length of Hair (in inches)
4.
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Time (in years)
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Lesson 11.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Distance from Home (in miles)
5.
Time (in minutes)
Money Spent Over Budget ($)
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6.
Time (in months)
Chapter 11 Skills Practice • 691
Lesson 11.4 Skills Practice
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Choose the graph that best represents each scenario. 7. Carla filled a mug with tea. Every few minutes Carla took a drink from the mug.
a.
b.
c.
The graph that best represents the scenario is c.
8. Marcel was playing basketball. The basketball sprung a leak and the air steadily drained out of the basketball.
a.
b.
c.
9. Carissa was jogging in the park with her dog. Twice during their jog they slowed to a walk to rest before continuing to jog at a faster pace. a.
b.
c. © 2011 Carnegie Learning
692 • Chapter 11 Skills Practice
Lesson 11.4 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 10. Jessica filled her little brother’s baby pool in the backyard. As her brother played in the pool, he dumped buckets of water out of the pool. a.
b.
c.
11. Jamal was riding his bike. When he rode up a hill, his speed decreased. When he rode down a hill, his speed increased. a.
b.
c.
12. Lauren released a helium balloon outside. The balloon rose at a constant rate. b.
c.
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a.
Chapter 11 Skills Practice • 693
Lesson 11.4 Skills Practice
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Draw a graph to represent each scenario. Label the axes with the appropriate quantities. 13. Natasha and her family took a 3 day trip to her grandmother’s house. On the first day they drove 300 miles. On the second day they drove 350 miles. On the third day they drove the remaining 200 miles. 1000 900
Distance (in miles)
800 700 600 500 400 300 200 100 0
1
2 Time (in days)
3
4
14. Belinda’s cell phone plan charges $30 per month plus $0.10 per text message sent. In January, Belinda sent 75 text messages. In February, Belinda sent 50 text messages.
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In March, Belinda sent 100 text messages.
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Lesson 11.4 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 15. Nina is draining a 1200 gallon pool with a garden hose. After 2 hours, Nina finds that half of the water has drained out of the pool, but the garden hose becomes clogged and stops draining. It takes Nina an hour to clear the clog, and the pool begins to drain again. After 5 hours the pool is completely drained.
16. During a snow storm, light snow begins to fall and accumulates 1 inch in 3 hours. Then heavy snow squalls dump 6 more inches of snow in 2 hours. Finally light snow flurries add another inch
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of snow in 4 hours.
Chapter 11 Skills Practice • 695
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696 • Chapter 11 Skills Practice
