Deck 2: The Rectangular Coordinate System, Lines, and Circles

Question 1

Sketch the graph for the equation by plotting points.
$$y = 8 x ^ { 2 } - 1 , ( - 1,7 )$$

A)Yes
B)No

Answer 1

A

Question 2

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
(1, -5) A) Quadrant I

B) Quadrant II

C) Quadrant III

D) Quadrant IV

Answer 2

D

Question 3

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
(-1, -5)

A) Quadrant III

B) Quadrant IV

C) Quadrant II

D) Quadrant III

Answer 3

D

Question 4

Determine whether the indicated ordered pair lies on the graph of the given equation.
A = (3, 5); B = (9, 3) A) $( 4,6 )$
В) $( 6,4 )$
C) $( 12,8 )$
D) $( - 6,2 )$

Question 5

Determine whether the indicated ordered pair lies on the graph of the given equation.
y = |x|, (3, -3)

A)Yes
B)No

Question 6

Determine whether the indicated ordered pair lies on the graph of the given equation.
A = (7, 1); B = (-16, -16) A) $( - 9 , - 15 )$
B) $\left( \frac { 23 } { 2 } , \frac { 17 } { 2 } \right)$
C) $\left( - \frac { 9 } { 2 } , - \frac { 15 } { 2 } \right)$
D) $( 9,15 )$

Question 7

Sketch the graph for the equation by plotting points.
$$y = 9 x ^ { 2 } + 1 , ( - 1 , - 8 )$$

A)Yes
B)No

Question 8

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
(-4, 6)

A) Quadrant II

B) Quadrant I

C) Quadrant III

D) Quadrant IV

Question 9

Sketch the graph for the equation by plotting points.
x2 + 9y = 9

A)

B)

C)

D)

Question 10

Sketch the graph for the equation by plotting points.
$$y = \sqrt { x } - 4 , ( 9 , - 1 )$$

A)Yes
B)No

Question 11

The function f is one-to-one. State the domain and the range of f and f-1. Write the domain and range in set-builder notation.
(6, 0)

A) Quadrant II

B) $y$ -axis

C) $x$ -axis

D) $x$ -axis

Question 12

Sketch the graph for the equation by plotting points.
$$y = | x | , ( - 3,3 )$$

A)Yes
B)No

Question 13

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
(0, 4)

A) $x$ -axis

B) Quadrant II

C) $y$ -axis

D) $y$ -axis

Question 14

The function f is one-to-one. State the domain and the range of f and f-1. Write the domain and range in set-builder notation.
4x + 2y = 8

A)

B)

C)

D)

Question 15

Determine whether the indicated ordered pair lies on the graph of the given equation.
A = (y, 2); B = (0, 8) A) $\left( \frac { y } { 2 } , 5 \right)$
B) $( y , 5 )$
C) $( \mathrm { y } , 10 )$
D) $\left( - \frac { y } { 2 } , 6 \right)$

Question 16

The function f is one-to-one. State the domain and the range of f and f-1. Write the domain and range in set-builder notation.
y = x + 3

A)

B)

C)

D)

Question 17

Determine whether the indicated ordered pair lies on the graph of the given equation.
A = (5, -9); B = (-2, -3) A) $\left( \frac { 3 } { 2 } , - 6 \right)$
B) $\left( \frac { 7 } { 2 } , - 3 \right)$
C) $( 3 , - 12 )$
D) $( 7 , - 6 )$

Question 18

The function f is one-to-one. State the domain and the range of f and f-1. Write the domain and range in set-builder notation.
y = 2x - 6

A)

B)

C)

D)

Question 19

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
(2, 3)

A) Quadrant II

B) Quadrant IV

C) Quadrant I

D) Quadrant I

Question 20

Sketch the graph for the equation by plotting points.
$$y = \sqrt { x } - 4 , ( 4,0 )$$

A)Yes
B)No

Question 21

Find the distance d(A, B)between the points A and B.
A = (-6, -7); B = (0, -5); C = (-1, -10)

A)Yes
B)No

Question 22

Determine whether the points A, B, and C form a right triangle.
Center (0, -5), r = 7 A) $( x + 5 ) ^ { 2 } + y ^ { 2 } = 49$
В) $( x - 5 ) ^ { 2 } + y ^ { 2 } = 49$
C) $x ^ { 2 } + ( y + 5 ) ^ { 2 } = 49$
D) $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 7$

Question 23

Find the midpoint of the line segment joining the points A and B.
A = (9y, 9); B = (10y, 8) A) $( 19 y , 17 )$
B) $( y , 1 )$
C) $\left( \frac { 19 \mathrm { y } } { 2 } , \frac { 17 } { 2 } \right)$
D) $\left( \frac { 17 y } { 2 } , \frac { 19 } { 2 } \right)$

Question 24

Determine whether the points A, B, and C form a right triangle.
A = (-7, -3); B = (-1, -1); C = (5, -8)

A)Yes
B)No

Question 25

Find the center and radius of the circle with the given equation.
$$( x + 5 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 144$$

A) Center $( - 5,10 ) , \mathrm { r } = 12$
B) Center $( 10 , - 5 ) , \mathrm { r } = 144$
C) Center $( - 5,10 ) , \mathrm { r } = 144$
D) Center $( 10 , - 5 ) , \mathrm { r } = 12$

Question 26

Determine whether the points A, B, and C form a right triangle.
Center (5, 7), r = 12 A) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 144$
B) $( \mathrm { x } + 5 ) ^ { 2 } + ( \mathrm { y } + 7 ) ^ { 2 } = 12$
C) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 12$
D) $( x + 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 144$

Question 27

Find the distance d(A, B)between the points A and B.
A = (-6, 7); B = (-4, 11); C = (-2, 10)

A)Yes
B)No

Question 28

Find the midpoint of the line segment joining the points A and B.
A(-1, 6); B(2, 9); C( 4, 1); D(7, 4)

A)Yes
B)No

Question 29

Determine whether the points A, B, C and D form a parallelogram.
A = (4, 4); B = (4, 2)

A)2
B)3
C)1 $$\text { D) } \sqrt { 2 }$$

Question 30

Determine whether the points A, B, C and D form a parallelogram.
A = (0, 0); B = (-2, 5) A) $\sqrt { 29 }$
B) $\sqrt { 7 }$
C) 3
D) 29

Question 31

Determine whether the points A, B, and C form a right triangle.
The endpoints of a diameter are (3, 6)and (7, 6). A) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 4$
B) $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 4$
C) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 2$
D) $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 2$

Question 32

Find the distance d(A, B)between the points A and B.
A = (-3, -4); B = (3, -6) A) $32 \sqrt { 2 }$
B) 8
C) 32
D) $2 \sqrt { 10 }$

Question 33

Determine whether the points A, B, C and D form a parallelogram.
A(-2, 10); B(1, 9); C(3, 1); D(6, 4)

A)Yes
B)No

Question 34

Find the center and radius of the circle with the given equation.
$$x ^ { 2 } + y ^ { 2 } = 9$$

A) Center $( 3,3 ) , r = 3$
B) Center $( 0,0 ) , r = 3$
C) Center $( 3,3 ) , r = 9$
D) Center $( 0,0 ) , r = 9$

Question 35

Determine whether the points A, B, C and D form a parallelogram.
A = (1, 5); B = (-3, -2) A) $\sqrt { 33 }$
B) 3
C) 28
D) $\sqrt { 65 }$

Question 36

Determine whether the points A, B, C and D form a parallelogram.
A = (0, -2); B = (-7, -2)

A)7 $$\text { B) } \sqrt { 53 }$$
C)2
D)49

Question 37

Determine whether the points A, B, C and D form a parallelogram.
A = (7, -5); B = (3, -3) A) $12 \sqrt { 3 }$
B) 6
C) 12
D) $2 \sqrt { 5 }$

Question 38

Determine whether the points A, B, C and D form a parallelogram.
A = (4, 2); B = (1, 6)

A)10
B)5
C)25
D)6

Question 39

Determine whether the points A, B, and C form a right triangle.
Center (0, 0), r = 2 A) $x ^ { 2 } + y ^ { 2 } = 2$
B) $x ^ { 2 } + y ^ { 2 } = 4$
C) $( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4$
D) $( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 2$

Question 40

Find the distance d(A, B)between the points A and B.
A = (-8, 3); B = (-5, 3); C = (-5, 12)

A)Yes
B)No

Question 41

Graph the equation.
$$x ^ { 2 } + y ^ { 2 } = 9$$

A)

B)

C)

D)

Question 42

Write the standard form of the equation of the circle.
$$x ^ { 2 } + y ^ { 2 } = 9$$

A)The x-intercept is x = 9, and the y-intercept is y = 9.
B)The two x-intercepts are x = 9 and x = -9, and the two y-intercepts are y = 9 and y = -9.
C)The two x-intercepts are x = 3 and x = -3, and the two y-intercepts are y = 3 and y = -3.
D)The x-intercept is x = 3, and the y-intercept is y = 3.

Question 43

Find the center (h, k)and radius r of the circle. Graph the circle.
$$x ^ { 2 } + y ^ { 2 } + 2 x + 12 y + 28 = 0$$

A) Center $( - 1,6 ) , r = 3$

B) Center $( 1,6 ) , \mathrm { r } = 3$

C) Center $( 1 , - 6 ) , \mathrm { r } = 3$

D) Center $( - 1 , - 6 ) , r = 3$

Question 44

Write the standard form of the equation of the circle.
$$121 x ^ { 2 } + 121 y ^ { 2 } - 66 x - 132 y - 438 = 0$$

A)The x-intercept is x ≈41.7, and the y-intercept is y ≈40.65.
B)There are no intercepts.
C)The two x-intercepts are x ≈4.12 and x ≈-3.57, and the two y-intercepts are y ≈4.5 and y ≈-3.41.
D)The two x-intercepts are x ≈2.19 and x ≈-1.65, and the two y-intercepts are y ≈2.52 and y ≈-1.43.

Question 45

Find the center and radius of the circle with the given equation.
$$x ^ { 2 } + 8 x + 16 + ( y + 9 ) ^ { 2 } = 81$$

A)Center (-4, -9), r = 9
B)Center (4, 9), r = 81
C)Center (-9, -4), r = 9
D)Center (9, 4), r = 81

Question 46

Graph the equation.
$$x ^ { 2 } + ( y - 2 ) ^ { 2 } = 9$$

A)

B)

C)

D)

Question 47

Write the standard form of the equation of the circle.
A)

B)

C)

D)

Question 48

Write the standard form of the equation of the circle.
$$( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 28$$

A)The two x-intercepts are x ≈8.9 and x ≈-0.9, and the two y-intercepts are y ≈1.46 and y ≈-5.46.
B)The two x-intercepts are x ≈0.9 and x ≈-8.9, and the two y-intercepts are y ≈5.46 and y ≈-1.46.
C)There are no intercepts.
D)The two x-intercepts are x ≈1.66 and x ≈-9.66, and the two y-intercepts are y ≈8.63 and y ≈-4.63.

Question 49

Find the center and radius of the circle with the given equation.
$$x ^ { 2 } - 12 x + 36 + y ^ { 2 } - 8 y + 16 = 4$$

A) Center $( 6,4 ) , r = 2$
B) Center $( - 4 , - 6 ) , r = 4$
C) Center $( 4,6 ) , \mathrm { r } = 2$
D) Center $( - 6 , - 4 ) , \mathrm { r } = 4$

Question 50

Write the standard form of the equation of the circle.
$$( x - 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$$

A)The two x-intercepts are x = 7 and x = -7, and the two y-intercepts are y = 3 and y = -3.
B)The x-intercept is x = 4, and the y-intercept is y = -9.
C)There are no intercepts.
D)The two x-intercepts are x = 4 and x = -4, and the two y-intercepts are y = 3 and y = -3.

Question 51

Find the center and radius of the circle with the given equation.
$$x ^ { 2 } + ( y + 4 ) ^ { 2 } = 25$$

A) Center $( - 4,0 ) , r = 5$
B) Center $( 0 , - 4 ) , r = 5$
C) Center $( 0 , - 4 ) , \mathrm { r } = 25$
D) Center $( - 4,0 ) , \mathrm { r } = 25$

Question 52

Find the center and radius of the circle with the given equation.
$$( x - 4 ) ^ { 2 } + y ^ { 2 } = 16$$

A) Center $( 0,4 ) , r = 16$
B) Center $( 4,0 ) , r = 16$
C) Center $( 4,0 ) , \mathrm { r } = 4$
D) Center $( 0,4 ) , \mathrm { r } = 4$

Question 53

Find the slope of the line.
A) 6
B) $\frac { 1 } { 6 }$
C) $- 6$
D) $- \frac { 1 } { 6 }$

Question 54

Find the intercepts of the circle. Round to the nearest hundredth, when necessary.
$$x ^ { 2 } + y ^ { 2 } + 14 x + 10 y = - 25$$

A) Center $( - 7 , - 5 ) , r = 7$
B) Center $( 5,7 ) , r = 49$
C) Center $( - 5 , - 7 ) , r = 7$
D) Center $( 7,5 ) , r = 49$

Question 55

Find the intercepts of the circle. Round to the nearest hundredth, when necessary.

A)-1
B)6
C)1
D)-6

Question 56

Find the intercepts of the circle. Round to the nearest hundredth, when necessary.

A)1
B)-1
C)-6
D)6

Question 57

Graph the equation.
$$( x + 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$$

A)

B)

C)

D)

Question 58

Find the intercepts of the circle. Round to the nearest hundredth, when necessary.
A) $- 6$
B) $\frac { 1 } { 6 }$
$C ) = \frac { 1 } { 6 }$
D) 6

Question 59

Find the center (h, k)and radius r of the circle. Graph the circle.
A) Center $( - 4,2 ) , r = 3$


B) Center $( - 4 , - 2 ) , r = 3$

C) Center $( 4 , - 2 ) , r = 3$

D) Center $( 4,2 ) , \mathrm { r } = 3$

Question 60

Find the center and radius of the circle with the given equation.
$$x ^ { 2 } + y ^ { 2 } - 10 x + 2 y + 26 = 16$$

A) Center $( - 5,1 ) , r = 16$
B) Center $( 5 , - 1 ) , r = 4$
C) Center $( - 1,5 ) , r = 4$
D) Center $( 1 , - 5 ) , r = 16$

Question 61

Find the slope of the line.
(5, 0)and (0, 3) A) $- \frac { 3 } { 5 }$
B) $\frac { 5 } { 3 }$
C) $\frac { 3 } { 5 }$
D) $- \frac { 5 } { 3 }$

Question 62

Find the slope of the line containing the two points.
Slope = 0; line passes through the point (8, -4)

A)

B)

C)

D)

Question 63

Find the slope of the line containing the two points.
$\text { Slope }=-\frac{3}{4} ; \text { line passes through the point }(4,0)$


A)

B)

C)

D)

Question 64

Find the slope of the line containing the two points.
(2, -4)and (-3, -4) A) 0
B) $- 5$
C) $\frac { 1 } { 5 }$
D) undefined

Question 65

Find the slope of the line.
(5, -3)and (6, -5) A) $- \frac { 1 } { 2 }$
B) 2
C) $\frac { 1 } { 2 }$
D) $- 2$

Question 66

Find the slope of the line containing the two points.
$$\text { Slope } = \frac { 4 } { 5 } ; \text { line passes through the point } ( 0,4 )$$

A)

B)

C)

D)

Question 67

Find the slope of the line containing the two points.
Slope = 1; line passes through the point (-4, -6) A)

B)

C)

D)

Question 68

Sketch the line with the given slope that passes through the indicated point.
Slope $= \frac { 5 } { 2 } ;$ line passes through the point $( - 3,5 )$

A) $y + 3 = \frac { 5 } { 2 } ( x - 5 )$
B) $y - 5 = \frac { 5 } { 2 } ( x + 3 )$
C) $y + 5 = \frac { 5 } { 2 } ( x - 3 )$
D) $x + 5 = \frac { 5 } { 2 } ( y - 3 )$

Question 69

Find the point-slope equation for the line with the given properties.
Slope $= - \frac { 2 } { 5 } ;$ line passes through the point $( 4,5 )$

A) $y - 5 = - \frac { 2 } { 5 } ( x + 4 )$
B) $y - 5 = \frac { 2 } { 5 } ( x - 4 )$
C) $y + 5 = - \frac { 2 } { 5 } ( x + 4 )$
D) $y - 5 = - \frac { 2 } { 5 } ( x - 4 )$

Question 70

Find the slope of the line.
(-5, -3)and (-5, -2)

A)- 1
B)1
C)0
D)undefined

Question 71

Find the point-slope equation for the line with the given properties.
(5, -6)and (7, 1) A) $y + 6 = - \frac { 11 } { 6 } ( x - 5 )$ or $y - 1 = - \frac { 11 } { 6 } ( x - 7 )$
B) $y + 6 = \frac { 7 } { 2 } ( x - 5 )$ or $y - 1 = \frac { 7 } { 2 } ( x - 7 )$
C) $y - 6 = \frac { 7 } { 2 } ( x + 5 )$ or $y + 1 = \frac { 7 } { 2 } ( x + 7 )$
D) $y + 6 = \frac { 11 } { 6 } ( x - 5 )$ or $y - 1 = \frac { 11 } { 6 } ( x - 7 )$

Question 72

Find the slope of the line containing the two points.
$$\text { Slope } = \frac { 2 } { 5 } \text {; line passes through the point } ( - 8,5 )$$

A)

B)

C)

D)

Question 73

Find the slope of the line.
(8, -4)and (-7, 9) A) $- \frac { 15 } { 13 }$
В) $\frac { 13 } { 15 }$
C) $\frac { 15 } { 13 }$
D) $- \frac { 13 } { 15 }$

Question 74

Sketch the line with the given slope that passes through the indicated point.
Slope is undefined; line passes through the point (-7, 10)

A)

B)

C)

D)

Question 75

Find the point-slope equation for the line with the given properties.
(-2, 15)and (4, -9)

A)y + 15 = -4(x + 2)or y + 9 = -4(x + 4)
B)y - 15 = -4(x + 2)or y + 9 = -4(x - 4)
C)y + 15 = -4(x - 2)or y - 9 = -4(x + 4)
D)y - 15 = -4(x - 2)or y - 9 = -4(x - 4)

Question 76

Find the point-slope equation for the line with the given properties.
(7, 9)and (4, 1) A) $y + 9 = \frac { 8 } { 3 } ( x + 7 )$ or $y + 1 = \frac { 8 } { 3 } ( x + 4 )$
B) $y - 9 = \frac { 2 } { 3 } ( x - 7 )$ or $y - 1 = \frac { 2 } { 3 } ( x - 4 )$
C) $y + 9 = \frac { 2 } { 3 } ( x + 7 )$ or $y + 1 = \frac { 2 } { 3 } ( x + 4 )$
D) $y - 9 = \frac { 8 } { 3 } ( x - 7 )$ or $y - 1 = \frac { 8 } { 3 } ( x - 4 )$

Question 77

Find the point-slope equation for the line with the given properties.
(-4, -8)and (2, 16)

A)y - 8 = 4(x - 4)or y - 16 = 4(x - 2)
B)y + 8 = 4(x - 4)or y - 16 = 4(x + 2)
C)y - 8 = 4(x - 4)or y + 16 = 4(x + 2)
D)y + 8 = 4(x + 4)or y - 16 = 4(x - 2)

Question 78

Find the slope of the line containing the two points.
Slope = - 1; line passes through the point (-2, -4)

A)

B)

C)

D)

Question 79

Find the slope of the line containing the two points.
$$\text { Slope } = - \frac { 1 } { 3 } ; \text { line passes through the point } ( 0,2 )$$

A)

B)

C)

D)

Question 80

Find the slope of the line containing the two points.
A)

B)


C)

D)