College algebra 2nd edition kirk trigsted test bank

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
1) (5, 4)
1) _______

A) Quadrant IV

B) Quadrant I

C) Quadrant II

D) Quadrant I

2) (-5, 2)

2) _______


A) Quadrant IV

B) Quadrant I

C) Quadrant II

D) Quadrant III

3) (2, -5)

A) Quadrant III

C) Quadrant I

3) _______

B) Quadrant IV


D)

Q
ua
dr
an
t
II

4) (-2, -5)

A) Quadrant III

C) Quadrant IV

4) _______

B) Quadrant II


D)

Q
ua

dr
an
t
III

5) (0, -1)

A) x-axis

C) y-axis

5) _______

B) Quadrant II


D)

yax
is

6) (-4, 0)

6) _______

A) x-axis

B) x-axis

C) y-axis

D) Quadrant II


Sketch the graph for the equation by plotting points.
7) y = x + 6

7) _______

A)

B)

C)

D)

8) y = 2x - 4

A)

8) _______


B)

C)

D)

9) 2x + 5y = 10

A)

C)

9) _______

B)


D)

10) x2 + 9y = 9

10) ______

A)

B)

C)

D)

Determine whether the indicated ordered pair lies on the graph of the given equation.


11) y = 7 - 1, (-1, 6)
A) Yes

11) ______
B) No

12) y = 9 + 1, (-1, - 8)
A) Yes

12) ______
B) No

13) y =
- 2, (9, 1)
A) Yes

13) ______
B) No

14) y =
- 4, (4, 0)
A) Yes

14) ______
B) No

15) y = |x|, (- 8, 8)
A) Yes

B) No

16) y = |x|, (6, - 6)

A) Yes

B) No

15) ______

16) ______

Find the midpoint of the line segment joining the points A and B.
17) A = (7, 1); B = (9, 9)
A)
B)
C) (-2, -8)
18) A = (1, -3); B = (-4, 5)
A)

19) A = (7, 1); B = (-16, -16)
A)

17) ______
D) (16, 10)
18) ______

B)

C) (5, -8)

D) (-3, 2)

19) ______

B) (-9, -15)

C) (9, 15)

D)

20) A = (a, 3); B = (0, 7)
A) (a, 10)

B)

C)

D)

21) A = (8 b, 6); B = (9 b, 3)
A) (b, 3)

B)

C) (17 b, 9)

D)

20) ______

21) ______

Determine whether the points A, B, C and D form a parallelogram.
22) A(3, 3); B(6, 6); C( 8, -2); D(11, 1)

A) Yes
B) No
23) A(2, 8); B(5, 8); C(7, 0); D(10, 3)
A) Yes
Find the distance d(A, B) between the points A and B.
24) A = (5, 5); B = (5, -5)
A) 10
B) 9
25) A = (2, 3); B = (-10, -2)
A) 169

22) ______

23) ______
B) No

24) ______
C)

D) 11
25) ______

B) 13

C) 26

D) 14


26) A = (0, 2); B = (-3, 2)

A) 9

B) 2

C) 3

D)

27) A = (0, 0); B = (-3, 8)
A) 5

B) 73

C)

D)

26) ______

27) ______

28) A = (6, 2); B = (-4, -1)
A)

28) ______
B) 7

29) A = (2, -7); B = (4, -3)
A) 2

C) 30

D)
29) ______

B) 12

30) A = (-1, -2); B = (6, -3)
A) 5

C) 2

D) 12
30) ______

B) 8

C) 48

D) 48

Determine whether the points A, B, and C form a right triangle.
31) A = (2, -3); B = (5, -3); C = (5, 5)
A) Yes
B) No
32) A = (-1, -2); B = (1, 2); C = (3, 1)
A) Yes

B) No

33) A = (7, 12); B = (13, 14); C = (12, 9)
A) Yes

B) No

34) A = (-3, -2); B = (3, 0); C = (9, -7)
A) Yes
Write the standard form of the equation of the circle.
35) Center (0, 0), r = 3
A)
+
=9
C)

+

=3

36) Center (5, 8), r = 8
A) (x - 5)2 + (y - 8)2 = 64

33) ______

34) ______
B) No

35) ______
B)

+

=3

D)

+

=9

B) (x + 5)2 + (y + 8)2 = 8
D) (x + 5)2 + (y + 8)2 = 64

37) Center (6, 0), r = 10
A) x2 + (y - 6)2 = 10

37) ______
B) (x - 6)2 + y2 = 100
D) x2 + (y + 6)2 = 10

C) (x + 6)2 + y2 = 100
38) Center (0, -3), r = 2
A) (x + 3)2 + y2 =

38) ______
B) (x - 3)2 + y2 = 4

4
39) The endpoints of a diameter are (3, 5) and (9, 5).
A)
+

=3
+

32) ______

36) ______

C) (x - 5)2 + (y - 8)2 = 8

C)

31) ______

=9

C) x2 + (y + 3)2 =
4

D) x2 + (y - 3)2 = 2

39) ______
B)

+

=9

D)

+

=3


Find the center and radius of the circle with the given equation.
40)
+
= 16
A) Center (4, 4), r = 16
C) Center (0, 0), r = 4
41) (x - 8)2 + (y - 3)2 = 144
A) Center (3, 8), r = 144
C) Center (8, 3), r = 12
42) (x - 4)2 + y2 = 144
A) Center (0, 4), r = 12
C) Center (4, 0), r = 12
43) x2 + (y - 1)2 = 100
A) Center (1, 0), r = 100
C) Center (0, 1), r = 100

B) Center (4, 4), r = 4
D) Center (0, 0), r = 16
41) ______
B) Center (3, 8), r = 12
D) Center (8, 3), r = 144
42) ______
B) Center (0, 4), r = 144
D) Center (4, 0), r = 144
43) ______
B) Center (0, 1), r = 10

D) Center (1, 0), r = 10

Graph the equation.
44)
+
= 16

A)

C)

40) ______

44) ______

B)


D)

45)

+

45) ______

=4

A)

B)

C)

D)

46) x2 + (y - 2)2 = 25


46)

___
___

A)

B)

C)

D)

47)

+

A)

=4

47) ______


B)

C)

D)

Find the intercepts of the circle. Round to the nearest hundredth, when necessary.
48)
+
=9

48) ______

A)
B)
C)
D)

The two x-intercepts are x = 3 and x = - 3, and the two y-intercepts are y = 3 and y = - 3.
The x-intercept is x = 9, and the y-intercept is y = 9.
The two x-intercepts are x = 9 and x = - 9, and the two y-intercepts are y = 9 and y = - 9.
The x-intercept is x = 3, and the y-intercept is y = 3.
49) ______

A)
B)
C)

D)

+
=4
The two x-intercepts are x = 4 and x = - 4, and the two y-intercepts are y = 2 and y = - 2.
The two x-intercepts are x = 6 and x = - 6, and the two y-intercepts are y = 2 and y = - 2.
There are no intercepts.
The x-intercept is x = 4, and the y-intercept is y = - 4.
+
= 24
The two x-intercepts are x ≈ 2.29 and x ≈ -8.29, and the two y-intercepts are y ≈ 7.74 and y ≈
-3.74.
There are no intercepts.
The two x-intercepts are x ≈ 7.47 and x ≈ -1.47, and the two y-intercepts are y ≈ 1.87 and y ≈
-5.87.
The two x-intercepts are x ≈ 1.47 and x ≈ -7.47, and the two y-intercepts are y ≈ 5.87 and y ≈
-1.87.

50) ______

51) 121 + 121
- 66x - 110y - 410 = 0
A) The two x-intercepts are x ≈ 3.99 and x ≈ -3.45, and the two y-intercepts are y ≈ 4.25 and y ≈
-3.34.

51) ______

49)

50)

A)
B)
C)
D)


B) The x-intercept is x ≈ 40.32, and the y-intercept is y ≈ 39.7.
C) There are no intercepts.
D) The two x-intercepts are x ≈ 2.13 and x ≈ -1.59, and the two y-intercepts are y ≈ 2.35 and y ≈
-1.44.
Find the center (h, k) and radius r of the circle. Graph the circle.
52) x2 + y2 - 4x - 2y - 20 = 0

A) Center (2, 1), r = 5

B) Center (-2, 1), r = 5

C) Center (2, -1), r = 5

D) Center (-2, -1), r = 5

53) x2 + y2 + 10x + 6y + 30 = 0

52) ______


53)

___
___

A) Center (-5, -3), r = 2

B) Center (5, -3), r = 2

C) Center (-5, 3), r = 2

D) Center (5, 3), r = 2

Find the center and radius of the circle with the given equation.
54) x2 - 8x + 16 + (y - 3)2 = 25
A) Center (-3, -4), r = 25
C) Center (-4, -3), r = 25
55) x2 + 14x + 49 + y2 - 10y + 25 = 9
A) Center (7, -5), r = 9
C) Center (-7, 5), r = 3
56) x2 + y2 - 8x - 4y + 20 = 81
A) Center (-2, -4), r = 81
C) Center (4, 2), r = 9
57) x2 + y2 - 2x + 8y = 32
A) Center (-1, 4), r = 49

54) ______

B) Center (3, 4), r = 5
D) Center (4, 3), r = 5
55) ______
B) Center (5, -7), r = 3
D) Center (-5, 7), r = 9
56) ______

B) Center (-4, -2), r = 81
D) Center (2, 4), r = 9
57) ______
B) Center (1, -4), r = 7


C) Center (4, -1), r = 49

D) Center (-4, 1), r = 7

Find the slope of the line.
58)

A)

58) ______

B) 2

C) - 2

D)

59)

59) ______

A) -1

B) -6

C) 6

D) 1

60)

60) ______

A) 1
61)

B) 6

C) -6

D) -1


61)

___
___

B) -4

A)

C)

D) 4

C)

D)

Find the slope of the line containing the two points.
62) (7, -7) and (-6, 7)
A)
B)

62) ______
-

63) (10, 0) and (0, 3)
A)

63) ______

B)

C)

D)
-

64) (6, 4) and (1, 1)
A)

64) ______

B)

C)

-

D)
-

65) (-3, 6) and (-3, 2)
A) 0

B)

C) -4

D) undefined

65) ______

66) (-2, -2) and (-6, -2)
A)

B) 0

C) -4

D) undefined

66) ______

Sketch the line with the given slope that passes through the indicated point.
67) Slope = - 2; line passes through the point (-5, 3)

A)

67) ______


B)

C)

D)

68)

68) ______
Slope =

A)

C)

; line passes through the point (-3, -5)

B)

D)

69) Slope = - 1; line passes through the point (-2, -2)

70)

69) ______

A)

B)

C)

D)

Slo
pe


70)

___
___

= ; line
passes
through
the point
(0, 6)

A)

B)

C)

D)

71) Slope = - 1; line passes through the point (0, 4)


71)

___
___

A)

B)

C)

D)

72) Slope = 1; line passes through the point (- 2, 0)

A)

72) ______

B)

C)

D)

73)

73) ______
Slope = -

A)

C)

; line passes through the point (3, 0)

B)


D)

74) Slope = 0; line passes through the point (-5, -10)

74) ______

A)

B)

C)

D)

75) Slope is undefined; line passes through the point (1, 2)


75)

___
___

A)

B)

C)

D)

Find the point-slope equation for the line with the given properties.
76)
Slope =
A)

; line passes through the point (3, -4)
B)

y+4=

(x - 3)

x-4=

76) ______

C)

(y + 3)

D)
y-4=

(x + 3)

77)

y-3=

(x + 4)
77) ______

Slope = A)

; line passes through the point (4, 2)

y+2=-

B)
(x + 4)

C)

y-2=-

(x + 4)

y-2=-

(x - 4)

D)
y-2=

(x - 4)

Find the equation of the line passing through the indicated two points. Write the equation in point-slope form.