1. Name the quadrant for the point (–7, –34).
A) I
B) II
C) III
D) IV
2. Name the quadrant for the point (–4, 3)
A) I
B) II
C) III
D) IV
3. Name the quadrant for the point (20, –50).
A) I
B) II
C) III
D) IV
4. Describe the line containing the points (–5, 12), (–48, 12), (3, 12).
A) vertical line
B) horizontal line
C) a line going up
D) a line going down
5. Describe the line containing the points (–10, 25), (–10, 50), (–10, 41).
A) vertical line
B) horizontal line
C) a line going up
D) a line going down
6. Describe the line containing the points (–24, –9), (25, 37), (34, 50).
A) vertical line
B) horizontal line
C) a line going up
D) a line going down
E) None of the above.
7. Describe the line containing the points (–49, 18), (–4, –27), (35, –66).
A) vertical line
B) horizontal line
C) a line going up
D) a line going down
8. Find the distance between the points (–5, 3) and (2, –3)
A)
B) 85
C) 13
D)
9. Find the distance between the points (10, –2) and (–2, 8).
A)
B)
C) 44
D) 244
10. Find the midpoint of the segment joining the points (–11, –10) and (3, –2)
A) (–4, –6)
B) (–7, –4)
C) (–6, –4)
D) (–8, –12)
11. Find the midpoint of the segment joining the points (–2, –10) and (7, 5).
A) (5, –5)
B) (2.5, –2.5)
C) (4.5, 7.5)
D) (–4.5, –7.5)
12. Calculate the distance (to two decimal places) and the midpoint between the segment joining
the points (2, 5) and (–3, 2).
13. Calculate the distance (to two decimal places) and the midpoint between the segment joining
the points (–6.7, –10) and (–0.4, –1.5).
14. Determine whether the triangle with the given vertices is a right triangle, an isosceles
triangle, neither, or both. (Recall that a right triangle satisfies the Pythagorean theorem and
an isosceles triangle has at least two sides of equal length.)
(1, 7), (–5, 8), and (–7, 6)
15. Determine whether the triangle with the given vertices is a right triangle, an isosceles
triangle, neither, or both. (Recall that a right triangle satisfies the Pythagorean theorem and
an isosceles triangle has at least two sides of equal length.)
(4, –6), (10, –1), and (12, –10)
16. Give the coordinates for the point in the graph.
17. Give the coordinates for the point in the graph.
A) (–1, –3)
B) (1, –3)
C) (1,3)
D) (–1,3)
18. Give the coordinates for the point in the graph.
19. Give the coordinates for the point in the graph.
A) (0, 4)
B) (0, –4)
C) (–4, 0)
D) 4
20. Calculate (to two decimal places) the perimeter of the triangle with the following vertices at
points A, B, and C.
21. Calculate (to two decimal places) the perimeter of the triangle with the following vertices at
points A, B, and C.
A) 16.71
B) 9.73
C) 94.00
D) –2.07
Answer Key - Chapter 2.1
1. C
2. B
3. D
4. B
5. A
6. E
7. D
8. A
9. A
10. A
11. B
12. distance 5.83, midpoint (–0.5, 3.5)
13. distance 10.58, midpoint (–3.55, –5.75)
14. neither
15. neither
16. (–4, –3)
17. A
18. (4, 0)
19. A
20. 30.47
21. A
1. Determine which point lies on the graph of the equation y = –9x2 – 8x + 12
A) (–373, 7)
B) (7, –373)
C) (–485, 7)
D) (7, –485)
2. Determine which point lies on the graph of the equation y = |8 – x| + 7.
A) (19, 4)
B) (4, 19)
C) (4, 11)
D) (0, 0)
3. Which of the following applies to the graph
?
A) symmetry with respect to the x-axis
B) symmetry with respect to the y-axis
C) symmetry with respect to the origin
D) no symmetry
4. Which of the following applies to the graph
A) symmety with respect to the x-axis
B) symmety with respect to the y-axis
C) symmety with respect to the origin
D) no symmetry
?
5. Which of the following applies to the graph y = 5x5?
A) symmety with respect to the x-axis
B) symmety with respect to the y-axis
C) symmety with respect to the origin
D) no symmetry
6. The point (–17, 9) lies on the graph that is symmetric about the x-axis. State the other point
that must also lie on the graph.
A) (17, 9)
B) (17, –9)
C) (–17, –9)
D) (9, –17)
7. The point (10, –3) lies on the graph that is symmetric about the x-axis. State the other point
that must also lie on the graph.
A) (10, 3)
B) (–10, –3)
C) (–10, 3)
D) (–3, 10)
8. The point (9, –3) lies on the graph that is symmetric about the y-axis. State the other point
that must also lie on the graph.
A) (–3, 9)
B) (9, 3)
C) (–9, –3)
D) (–9, 3)
9. The point (–9, –1) lies on the graph that is symmetric about the y-axis. State the other point
that must also lie on the graph.
A) (–1, –9)
B) (9, –1)
C) (–9, 1)
D) (9, 1)
10. The point (–6, 4) lies on the graph that is symmetric about the origin. State the other point
that must also lie on the graph.
A) (4, –6)
B) (6, 4)
C) (–6, –4)
D) (6, –4)
11. The point (–5, –7) lies on the graph that is symmetric about the origin. State the other point
that must also lie on the graph.
A) (–7, –5)
B) (5, 7)
C) (5, –7)
D) (–5, 7)
12. Use algebraic tests to determine whether the graph of the equation y = 3x6 + 9x3 is
symmetric with respect to the x-axis, y-axis, or origin.
A) x-axis
B) y-axis
C) origin
D) no symmetry
13. Use algebraic tests to determine whether the graph of the equation 10x2 + 4y2 = 36 is
symmetric with respect to the x-axis, y-axis, or origin.
A) x-axis
B) y-axis
C) origin
D) x-axis, y-axis, origin
14. Use algebraic tests to determine whether the graph of the equation y = | x | + 20 is
symmetric with respect to the x-axis, y-axis, or origin.
A) x-axis
B) y-axis
C) origin
D) no symmetry
15. The given point (–7, 8) lies on the graph that is symmetric about the x-axis, y-axis, and
origin. State the other points that must also lie on the graph.
16. Use algebraic tests to determine whether the graph 2x2 - 17y2 = 1 is symmetric with respect
to the x-axis, y-axis, or origin.
17. Use algebraic tests to determine whether the graph of y = 16 x3 - 19 x is symmetric with
respect to the x-axis, y-axis, or origin.
18. Plot the graph of the given equation.
x=
A)
y2
B)
C)
D)
19. The profit associated with making a particular product is given by the equation
y = –x2 + 10x – 16
where y represents the profit in millions of dollars and x represents the number of thousands
of units sold. (x = 1 corresponds to 1000 units and y = 1 corresponds to $1M.) Graph this
equation and determine how many units must be sold to break even (profit = 0). Determine
the range of units sold that correspond to making a profit.
A)
2,000 units or 8,000 units must be sold to break even
range of units sold that correspon to making a profit is 2,000 to 8,000
B)
2,000 units or 8,000 units must be sold to break even
range of units sold that correspon to making a profit is 2,000 to 8,000
C)
2,000 units or 8,000 units must be sold to break even
range of units sold that correspon to making a profit is from 0 to 2,000 or at least 8,000
D)
2,000 units or 8,000 units must be sold to break even
range of units sold that correspon to making a profit is from 0 to 2,000 or at least 8,000
20. Use symmetry to help you graph the equation.
21. Use symmetry to help you graph the equation.
A)
B)
C)
D)
22. Use symmetry to help you graph the equation.
A)
B)
C)
D)
23. Use symmetry to help you graph the equation.
A)
B)
C)
D)
24. Match the graph with the corresponding symmetry.
A) No symmetry
B) Symmetry with respect to the x-axis, y-axis, and origin
C) Symmetry with respect to the x-axis
D) Symmetry with respect to the origin
E) Symmetry with respect to the y-axis
Answer Key - Chapter 2.2
1. D
2. C
3. B
4. C
5. C
6. C
7. A
8. C
9. B
10. D
11. B
12. D
13. D
14. B
15. (–7, –8), (7, 8), (7, –8)
16. x-axis, y-axis, and origin
17. origin
18. B
19. A
20.
21. A
22. A
23. A
24. A
1. Find the slope of the line that passes through the points (–2, 3) and (7, –10).
A)
B)
C)
D)
2. Find the slope of the line that passes through the points (0, 5) and (0, 7)
A) 12
B) –2
C) undefined
D) 0
3. Find the slope of the line that passes through the points (4, 3) and (–6, 3).
A)
B) 10
C) undefined
D) 0
4. Find the slope for the equation x – 19y = 8.
A) 19
B) –19
C) 1/19
D) –1/19
5. Find the slope for the equation 11x + y = –5
A) –11
B) 11
C) 1/11
D) –1/11
6. Find the slope of the equation x = –10.
A) –10
B) 10
C) undefined
D) 0
7. Find the slope of the equation y = 17.
A) 17
B) 1/17
C) undefined
D) 0
8. Find the x- and y-intercepts for the equation 8x + 2y = 48.
A) x-intercept: (6, 0), y-intercept (0, 24)
B) x-intercept: (24, 0), y-intercept (0, 6)
C) x-intercept: (-6, 0), y-intercept (0, -24)
D) x-intercept: (-24, 0), y-intercept (0, -6)
9. Find the x- and y-intercepts of the equation 4x – 3y = 24.
A) x-intercept: (–6, 0), y-intercept: (0, 8)
B) x-intercept: (–8, 0), y-intercept: (0, 6)
C) x-intercept: (6, 0), y-intercept: (0, –8)
D) x-intercept: (0, 6), y-intercept: (–8, 0)
10. Find the x- and y-intercept for the equation y + 3 = 8.
A) no x-intercept, y-intercept: (0, 5)
B) no x-intercept, y-intercept: (0, 3)
C) no x-intercept, y-intercept: (0, 8)
D) x-intercept: (0,0), y-intercept: (0, 5)
11. Write the equation of the line given the slope m = –11 and y-intercept (0, 16).
A) y = 16x – 11
B) y = 11x +16
C) y = –11x – 16
D) y = –11x + 16
12. Write the equation of the line given the slope m = 1/10 and x-intercept (1/11, 0).
A) y =
x+
B) y =
x–
C) y =
x–
D) y =
x+
13. Write the equation of the line given the slope m = –4/7 and a point (–6, 3) that lies on the
line.
A) y =
x–3
B) y =
x+
C) y =
x–
D) y =
x–
14. Find the y- and x-intercepts and slope of the line 3x – 7y = 21, if they exist .
15. Find the equation of the line that passes through the point (0, 4) and is parallel to the line y +
12x = 19.
16. The cost of a one day car rental is the sum of the rental fee, $60, plus $0.19 per mile. Write
an equation that models the total cost associated with the car rental.
17. Find the equation of the line that passes through the point (–6, –8) and is parallel to the line
y –3x = 6. Express your answer in slope-intercept form, if possible.
18. Find the equation of the line that passes through the point (36, 7) and is perpendicular to the
line 2y + 9x = 4.
19. For the graph, determine the slope.
A)
B)
C)
D)
20. For the graph, determine the slope.
21. For the graph, determine the slope.
A)
B)
C)
D)
22. For the graph, determine the x- and y-intercepts.
23. For the graph, determine the x- and y-intercepts.
A) x-intercept : (3, 0), y-intercept :
B) x-intercept :
, y-intercept : (0, 3)
C) x-intercept : 3, y-intercept :
D) x-intercept :
, y-intercept : 3
24. For the graph, determine the slope.
25. For the graph, determine the slope.
A) undefined
B) 0
C) 2
D) –2
26. For the graph, determine the x- and y-intercepts.
27. For the graph, determine the x- and y-intercepts.
A) x-intercept : ( 0 , 0 )
y-intercept : ( 0 , 0 )
B) None
C) 0
D) Undefined
28. For the graph, identify (by inspection) (a) the x- and y-intercepts and (b) classify the line as
rising, falling, horizontal, or vertical.
29. For the graph, identify (by inspection) (a) the x- and y-intercepts and (b) classify the line as
rising, falling, horizontal, or vertical.
Answer Key - Chapter 2.3
1. B
2. C
3. D
4. C
5. A
6. C
7. D
8. A
9. C
10. A
11. D
12. B
13. C
14. (0, –3), (7, 0), m = 3/7
15. y = –12x + 4
16. y = 0.19x + 60
17. y = 3x + 10
18.
19. A
20.
21. A
22. x-intercept : (2, 0), y-intercept :
23. A
24. 0
25. A
26. x-intercept : ( 2 , 0 )
y-intercept :
none
27. A
28. (a) x-intercept : (4, 0), y-intercept :
(b) falling
29. (a) x-intercept : ( 3 , 0 )
y-intercept :
none
(b) vertical
1. Find the equation of the circle with radius 4 and center (–7, –9) in standard form.
A) (x – 7)2 + (y – 9)2 = 16
B) (x + 7)2 + (y + 9)2 = 4
C) (x + 7)2 + (y + 9)2 = 16
D) (x – 7)2 + (y – 9)2 = 4
2. Find the equation of the circle with radius 9 and center (–3, 19) in standard form.
A) (x + 3)2 + (y – 19)2 = 81
B) (x + 3)2 + (y + 19)2 = 81
C) (x + 3)2 + (y – 19)2 = 9
D) (x – 3)2 + (y + 19)2 = 81
3. Find the equation of the circle with radius 3
A) (x + 7)2 + (y - 20)2 = 99
B) (x – 7)2 + (y + 20)2 = 99
C) (x – 7)2 + (y + 20)2 = 3
D) (x – 7)2 + (y + 20)2 = 33
and center (7, –20) in standard form.
4. Find the equation of the circle with radius 8
A) x + y = 8
B) x2 + y2 = 80
C) x2 + y2 = 640
D) x2 + y2 = 8
and center (0, 0) in standard form.
5. Find the center and radius of the circle with equation (x – 5)2 + (y + 19)2 = 25.
A) center = (5, –19), r = 25
B) center = (5, –19), r = 5
C) center = (–5, 19), r = 5
D) center = (–5, 19), r = 25
6. Find the center and radius of the circle with equation (x + 4)2 + (y – 15)2 = 112.
A) center (4, –15), r = 112
B) center (4, –15), r = 4
C) center (–4, 15), r = 112
D) center (–4, 15), r = 4
7. Find the center and radius of the circle with equation x2 + y2 – 80 = 0.
A) center (0, 0), r = 40
B) center (0, 0), r = 0
C) center (0, 0), r = 4
D) center (0, 0), r = 80
8. Find the center and radius of the circle with equation x2 + (y + 19)2 = 25.
A) center (0, –19), r = 25
B) center (0, 19), r = 25
C) center (0, 19), r = 5
D) center (0, –19), r = 5
9. Find the center and radius of the circle with equation (x + 9)2 + y2 = 28.
A) center = (–9, 0), r = 28
B) center = (–9, 0), r = 2
C) center = (9, 0), r = 28
D) center = (9, 0), r = 2
10. The point (3, 0) lies on a circle centered at (–3, 3). Find the equation of the circle in
standard form.
A) (x + 3)2 + (y – 3)2 = 45
B) (x + 3)2 + (y – 3)2 = 36
C) (x – 3)2 + (y + 3)2 = 45
D) (x – 3)2 + (y + 3)2 = 36
11. The point (3, –2) lies on a circle centered at (0, 6). Find the equation in standard form.
A) x2 + (y – 6)2 = 73
B) x2 + (y + 6)2 = 73
C) (x + 6)2 + y2 = 73
D) (x – 6)2 + y2 = 73
12. The point (–3, –5) lies on a circle centered at (6, 4). Find the equation of the circle in
standard form.
A) (x + 6)2 + (y + 4)2 = 162
B) (x – 6)2 + (y – 4)2 = 162
C) (x – 6)2 + (y – 4)2 = 8
D) (x + 3)2 + (y + 5)2 = 162
13. Find the equation of the circle with radius 1 and center (3, –17) in standard form
14. Find the center and radius of the circle with equation (x – 1)2 + (y + 15)2 = 144
15. Transform the equation
square. State the center and radius.
into standard form by completing the
16. If a cellular phone tower has a reception radius of 180 miles and you live 90 miles south and
120 miles west of the tower, can you use your cell phone while at home?
Answer Key - Chapter 2.4
1. C
2. A
3. B
4. C
5. B
6. D
7. C
8. D
9. B
10. A
11. A
12. B
13. (x – 3)2 + (y + 17)2 = 1
14. (1, –15), 12
15.
, center
16. yes
, radius 8