Deck 1: Rectangular Coordinates

Question 1

Sketch a scatter plot of the data shown in the table. The table shows the number y of Wal-Mart stores for each year x from 2000 through 2007.
$$\begin{array} { | l | l | } \hline \text { Year, } x & \text { Number of stores, } y \\\hline 2000 & 3700 \\\hline 2001 & 4400 \\\hline 2002 & 4680 \\\hline 2003 & 5010 \\\hline 2004 & 5550 \\\hline 2005 & 6360 \\\hline 2006 & 6680 \\\hline 2007 & 7340 \\\hline\end{array}$$

A)? x: Year (0 ? 2000)
Y: Number of stores
B)? x: Year (0 ? 2000)
Y: Number of stores
C)? ?
X: Year (0 ? 2000)
Y: Number of stores
D)? x: Year (0 ? 2000)
Y: Number of stores
E)? x: Year (0 ? 2000)
Y: Number of stores

Answer 1

? x: Year (0 ? 2000)
Y: Number of stores

Question 2

A point is located five units below the x-axis and the coordinates of the point are equal.Find the coordinates of the point. ​

A)(-5,5)
B)(-5,0)
C)(5,-5)
D)(-5,-5)
E)(5,5)

Answer 2

(-5,-5)

Question 3

Determine the quadrant(s)in which (x,y)is located so that the condition(s)is (are)satisfied. ​
Y < -6
​

A)Quadrant II or IV
B)Quadrant III or IV
C)Quadrant IV
D)Quadrant I
E)Quadrant II

Answer 3

Quadrant III or IV

Question 4

Determine the quadrant(s)in which (x,y)is located so that the condition(s)is (are)satisfied. ​
X > 3 and y = 1
​

A)Quadrant III
B)Quadrant I
C)Quadrant III and IV
D)Quadrant II
E)Quadrant IV

Question 5

A point is located six units to the left of the y-axis and seven units above the x-axis.Find the coordinates of the point. ​

A)(-6,7)
B)(7,6)
C)(-6,-7)
D)(6,-7)
E)(6,7)

Question 6

Determine the quadrant(s)in which (x,y)is located so that the condition(s)is (are)satisfied. ​
X < -9 and - y > 6
​

A)Quadrant I
B)Quadrant II
C)Quadrant IV
D)Quadrant III
E)Quadrant I or IV

Question 7

Determine the quadrant(s)in which (x,y)is located so that the condition(s)is (are)satisfied. ​
X = -2 and y > 0
​

A)Quadrant IV
B)Quadrant II or IV
C)Quadrant II
D)Quadrant I
E)Quadrant III

Question 8

Plot the points below whose coordinates are given on a Cartesian coordinate system. ​
(5,2), (9,-6), (2,-4), (9,-5)
​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 9

​Plot the points in the Cartesian plane. ​
(2,6), (2.5,6), (3,-6), (-6,4.5)
​

A)​
B)​
C)​
D)​
E)​

Question 10

Determine the quadrant(s)in which (x,y)is located so that the condition(s)is (are)satisfied. ​
Xy < -4
​

A)Quadrant II or III
B)Quadrant I or III
C)Quadrant III or IV
D)Quadrant II or IV
E)Quadrant I or IV

Question 11

Determine the quadrant(s)in which (x,y)is located so that the condition(s)is (are)satisfied. ​
X > 7 and y < 0
​

A)Quadrant I and IV
B)Quadrant III
C)Quadrant I
D)Quadrant IV
E)Quadrant II

Question 12

Find the coordinates of the point labeled II.

A)(-4,-3)
B)(-4,3)
C)(3,4)
D)(4,3)
E)(-3,-4)

Question 13

Approximate the coordinates of the points.? ?

A) $A : \left( 6 , - \frac { 1 } { 2 } \right) , B : \left( \frac { 3 } { 4 } , 3 \right) , C : ( - 2,5 ) , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right)$
B) $A : \left( 6 , - \frac { 1 } { 2 } \right) , B : \left( \frac { 3 } { 4 } , - 1 \right) , C : ( - 2,5 ) , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right)$
C) $A : \left( 6 , - \frac { 1 } { 2 } \right) , B : \left( \frac { 3 } { 4 } , 0 \right) , C : ( - 2,5 ) , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right)$
D) $A : \left( 6 , - \frac { 1 } { 2 } \right) , B : \left( \frac { 3 } { 4 } , 1 \right) , C : ( - 2,5 ) , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right)$
E) $A : \left( 6 , - \frac { 1 } { 2 } \right) , B : \left( \frac { 3 } { 4 } , 2 \right) , C : ( - 2,5 ) , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right)$

Question 14

Plot the points in the Cartesian plane. ?? $$\left( 4 , - \frac { 1 } { 6 } \right) , \left( \frac { 5 } { 2 } , 5 \right) , ( - 3,3 ) , \left( \frac { 2 } { 5 } , - \frac { 2 } { 5 } \right)$$ ?

A)?
B) ?
C)
D) ?
E)

Question 15

Determine the quadrant(s)in which (x,y)is located so that the condition(s)is (are)satisfied. ​
X < -8 and y < -6
​

A)Quadrant I
B)Quadrant I and II
C)Quadrant III
D)Quadrant II
E)Quadrant IV

Question 16

Approximate the coordinates of the points.​

A)​A: (4,2),B: (-6,-6),C: (5,2),D: (6,-5)
B)​A: (1,2),B: (-6,-6),C: (5,2),D: (6,-5)
C)​​A: (2,2),B: (-6,-6),C: (5,2),D: (6,-5)
D)​​A: (3,2),B: (-6,-6),C: (5,2),D: (6,-5)
E)​​​A: (-1,2),B: (-6,-6),C: (5,2),D: (6,-5)

Question 17

Which label corresponds to the coordinates (-3,-5)?

A)VI
B)VIII
C)V
D)VII
E)none

Question 18

Find the coordinates for the point that is four units to the left of the y-axis and is six units up from the x-axis.

A)(-4,-6)
B)(4,-6)
C)(-4,6)
D)(6,6)
E)(4,6)

Question 19

Plot the points in the Cartesian plane. ​
(-4,1), (-5,-2), (5,4), (2,-4)
​

A)​
B)​
C)​
D)​
E)​

Question 20

Determine the quadrant(s)in which (x,y)is located so that the conditions(s)is (are)satisfied. ​
- x > 6 and y < -2
​

A)Quadrant III
B)Quadrant I
C)Quadrant II
D)Quadrant I or IV
E)Quadrant IV

Question 21

Find the distance between the points.(Round the answer to two decimal places)​ ​
​(9)5,-4.1), (-3.3,8.7)
​

A)8.7
B)9.5
C)327.68
D)3.3
E)18.10

Question 22

Find the distance between the points. ​
(-9,4), (3,-5)
​

A)4
B)15
C)9
D)3
E)225

Question 23

Show that the points form the vertices of the indicated polygon. ?
Right triangle: (6,2), (3,4), (-3,-5)
?

A) $( \sqrt { 25 } ) ^ { 2 } + ( \sqrt { 117 } ) ^ { 2 } = ( \sqrt { 130 } ) ^ { 2 }$
B) $( \sqrt { 7 } ) ^ { 2 } + ( \sqrt { 117 } ) ^ { 2 } = ( \sqrt { 130 } ) ^ { 2 }$
C) $( \sqrt { 11 } ) ^ { 2 } + ( \sqrt { 117 } ) ^ { 2 } = ( \sqrt { 130 } ) ^ { 2 }$
D) $( \sqrt { 13 } ) ^ { 2 } + ( \sqrt { 117 } ) ^ { 2 } = ( \sqrt { 130 } ) ^ { 2 }$
E) $( \sqrt { 40 } ) ^ { 2 } + ( \sqrt { 117 } ) ^ { 2 } = ( \sqrt { 130 } ) ^ { 2 }$

Question 24

Find the distance between the two points (-3,-1)and (13,29).

A)65
B)68
C)102
D)31
E)34

Question 25

Plot the following points and find the midpoint of the line segment joining the points. ​
(9,6), (5,6)
​

A)​ Midpoint: (7,6)
B)​ Midpoint: (7,6)
C)​ ​
Midpoint: (7,6)
D)​ Midpoint: (7,6)
E)​ Midpoint: (7,6)

Question 26

Find the midpoint between the two points (-19,9)and (11,13). ​

A)(-15,2)
B)(-15,11)
C)(-8,11)
D)(-4,2)
E)(-4,11)

Question 27

Find the distance between the points. ​
(-8,-5), (-2,3)
​

A)10​
B)100
C)2
D)5
E)8

Question 28

Plot the following points and find the distance between the points. ?
(-5,8), (7,2)
?

A)? Distance: $6 \sqrt { 5 }$
B)? Distance: $6 \sqrt { 5 }$
C) Distance: $6 \sqrt { 5 }$
D)? Distance: $6 \sqrt { 5 }$
E)? Distance: $6 \sqrt { 5 }$

Question 29

Find the distance between the two points (6,1)and (6,7).

A)1
B)13
C)12
D)11
E)6

Question 30

Plot the following points and find the distance between the points. ​
(11,3), (5,3)
​

A)​ Distance: 8
B)​ Distance: 6
C)​ Distance: 9
D)​ Distance: 10
E)​ Distance: 7

Question 31

Given points(-1,1),and (-11,-9)form the vertices of the base of a triangle,find a third point so that the three points form the vertices of an isosceles triangle. ​

A)(3,1)
B)(4,-15)
C)​(-15,-13)
D)​(3,5)
E)​(-6,-4)

Question 32

Show that the points form the vertices of the indicated polygon. ?
Isosceles triangle: (7,-6), (9,8), (-5,6)
?

A)Distances between the points: $$\sqrt { 37 } , \sqrt { 200 } , \sqrt { 288 }$$
B)Distances between the points: $\sqrt { 200 } , \sqrt { 200 } , \sqrt { 288 }$
C)Distances between the points: $\sqrt { 26 } , \sqrt { 200 } , \sqrt { 288 }$
D)Distances between the points: $$\sqrt { 43 } , \sqrt { 200 } , \sqrt { 288 }$$
E)Distances between the points: $\sqrt { 19 } , \sqrt { 200 } , \sqrt { 288 }$

Question 33

Plot the following points and find the distance between the points. ?
(3,8), (8,3)
?

A)? Distance: $5 \sqrt { 2 }$
B) Distance: $$5 \sqrt { 2 }$$
C) ?
Distance: $$5 \sqrt { 2 }$$
D) ?
Distance: $$5 \sqrt { 2 }$$
E)? Distance: $5 \sqrt { 2 }$

Question 34

Show that the points form the vertices of the indicated polygon. ?
Isosceles triangle: (7,1), (5,4), (2,6)
?

A)Distances between the points: $$\sqrt { 19 } , \sqrt { 13 } , \sqrt { 50 }$$
B)Distances between the points: $\sqrt { 13 } , \sqrt { 13 } , \sqrt { 50 }$
C)Distances between the points: $$\sqrt { 43 } , \sqrt { 13 } , \sqrt { 50 }$$
D)Distances between the points: $\sqrt { 26 } , \sqrt { 13 } , \sqrt { 50 }$
E)Distances between the points: $\sqrt { 37 } , \sqrt { 13 } , \sqrt { 50 }$

Question 35

Show that the points form the vertices of the indicated polygon. ?
Right triangle: (3,5), (5,6), (6,4)
?

A) $( \sqrt { 5 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$
B) $$( \sqrt { 31 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$$
C) $$( \sqrt { 7 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$$
D) $( \sqrt { 11 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$
E) $( \sqrt { 34 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$

Question 36

Sketch a scatter plot of the data shown in the table. The table shows the lowest temperature on record y (in degrees Fahrenheit)in Duluth,Minnesota for each month x where x = 1 represents from January.

$$\begin{array} { | l | l | } \hline \text { Months, } x & \text { Temperature, } y \\\hline 1 & - 46 \\\hline 2 & - 36 \\\hline 3 & - 23 \\\hline 4 & - 7 \\\hline 5 & 14 \\\hline 6 & 25 \\\hline 7 & 31 \\\hline 8 & 42 \\\hline 9 & 24 \\\hline 10 & 3 \\\hline 11 & - 26 \\\hline 12 & - 15 \\\hline\end{array}$$

A) x: Months (1 ? January)
Y: Temperature (in Fº)
B) x: Months (1 ? January)
Y: Temperature (in Fº)
C) ?
X: Months (1 ? January)
Y: Temperature (in Fº)
D) ?
X: Months (1 ? January)
Y: Temperature (in Fº)
E) x: Months (1 ? January)
Y: Temperature (in Fº)

Question 37

An airplane flies from one city in a straight line to another city,which is 360 kilometers north and 150 kilometers west of first city.How far does the plane fly? ​

A)150 km
B)390 km
C)255 km
D)360 km
E)350 km

Question 38

Given the points (-6,-8)and (4,-6).Find a third point so that the three points form the vertices of a right triangle. ​

A)(-16,4)
B)(-11,17)
C)(-6,-9)
D)(5,-6)
E)(4,6)

Question 39

Find the distance between the points.(Round the answer to two decimal places) ​
(-6)5,4.9), (-9.5,7.5)
​

A)15.76
B)9.5
C)7.5
D)3.97
E)6.5

Question 40

Find the distance between the two points (10,7)and (-5,7). ​

A)30
B)20
C)12
D)40
E)15

Question 41

)Given points(5,-11),and (11,-5)form the vertices of the base of a triangle,find a third point so that the three points form the vertices of an isosceles triangle. ​

A)(8,-8)
B)(11,-12)
C)​(6,-10)
D)(10,-6)
E)(10,-11)

Question 42

Find the midpoint of the line segment joining the points (3,6)and (9,-4). ​

A)(6,-10)
B)(12,2)
C)(6,1)
D)(-3,5)
E)(3,-5)

Question 43

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.​ ​ Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.
​

A)About 48%
B)About 58%
C)About 43%
D)About 53%
E)About 38%

Question 44

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern. ​

A)$24,905 million
B)$24,855 million
C)$24,755 million
D)$24,955 million
E)$24,805 million

Question 45

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis. ​
​

A)(-8,-3)
B)(8,-3)
C)(-3,8)
D)(3,-8)
E)(-3,-8)

Question 46

A soccer player passes the ball from a point that is 13 yards from the end line and 16 yards from the sideline.The pass is received by a teammate who is 48 yards from the same end line and 39 yards from the same sideline,as shown in the figure.How long is the pass?? (a,b): (13,16) (c,d): (48,39)
?

A) $\sqrt { 1754 }$ ? 44 yd
B) $\sqrt { 757 }$ ? 43 yd
C) $\sqrt { 1754 }$ ? 45 yd
D) $\sqrt { 1754 }$ ? 42 yd
E) $\sqrt { 1754 }$ ? 46 yd

Question 47

Find the coordinates of the vertices of the polygon in its new position. ​
Original coordinates of vertices: (6,5), (3,2), (4,2), (5,2)​
Shift: six units downward,two units to the left
​

A)(13,-1), (1,-4), (2,-4), (3,-4)
B)(10,-1), (1,-4), (2,-4), (3,-4)
C)(12,-1), (1,-4), (2,-4), (3,-4)
D)(4,-1), (1,-4), (2,-4), (3,-4)
E)(11,-1), (1,-4), (2,-4), (3,-4)

Question 48

The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008.Describe any trends in the data.From these trends,predict the number of performers elected in 2009.

A)The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore five performers will be elected in 2009.
B)The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore seven performers will be elected in 2009.
C)The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore eight performers will be elected in 2009.
D)The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore six performers will be elected in 2009.
E)The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore nine performers will be elected in 2009.

Question 49

Determine the quadrant(s)in which (x,y)is located so that the condition is satisfied. x = 2 and y < -8

A)quadrant II
B)quadrant IV
C)quadrants I and IV
D)quadrants II and IV
E)quadrants III and IV

Question 50

Find the coordinates of the vertices of the polygon in its new position. ​
Original coordinates of vertices: (-5,-3), (-3,6), (-5,-4), (-4,-7)
Shift: three units to the right,four units upward
​

A)(-2,1), (0,10), (-2,0), (-1,-3)
B)(1,1), (0,10), (-2,0), (-1,-3)
C)(2,1), (0,10), (-2,0), (-1,-3)
D)(3,1), (0,10), (-2,0), (-1,-3)
E)(4,1), (0,10), (-2,0), (-1,-3)

Question 51

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.​ ​ Approximate the lowest price of a gallon of whole milk shown in the graph.When did this occur?
​

A)$2.97 / gal;2001
B)$3.17 / gal;2002
C)$3.07 / gal;2003
D)$2.67 / gal;1997
E)$3.87 / gal;2004

Question 52

Find the midpoint of the line segment joining the points (5.5,4.3)and (13.6,-1.2). ​

A)(19.1,3.1)
B)(8.1,-5.5)
C)(-4.05,2.75)
D)(9.55,1.55)
E)(4.05,-2.75)

Question 53

A quarterback is standing in the middle of the field 41 yards from his goal line.He passes the ball to a player 8 yards to his left on the 26 yard line.How long was the pass? ​

A)42 yards
B)15 yards
C)27 yards
D)17 yards
E)67 yards

Question 54

Find the distance between the points (4,-3)and (11,-3). ?

A)10
B) $\sqrt { 7 }$
C)3
D) $\sqrt { 10 }$
E)7

Question 55

Plot the point (-3,1)on the Cartesian plane. ​

A)
B)
C)
D)
E)

Question 56

Use the Midpoint Formula to estimate the sales of Dollar Tree Stores,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Dollar tree
Year
Sales (in millions)
2003
2200
2007
4283

A)$3241.5 million
B)$3251.5 million
C)$3246.5 million
D)$3256.5 million
E)$3261.5 million

Question 57

Find the distance between the points (4,-5)and (9,0).Round the answer to the nearest tenth. ​

A)7.1
B)7.4
C)7.3
D)7.5
E)6.9

Question 58

Find the coordinates of the point C shown below.​ ​ ​

A)(-2,3)
B)(3,-2)
C)(-4,-5)
D)(-5,-4)
E)(-5,-2)

Question 59

Use the Midpoint Formula to estimate the sales of Big Lots,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Big Lots
Year
Sales (in millions)
2003
4174
2007
4700

A)$4700 million
B)$4457 million
C)$4174 million
D)$4437 million
E)$4447 million

Question 60

​Find the distance between the points.Round to the nearest hundredth,if necessary. ​
(-8,-8), (-1,9)
​

A)​19.24
B)​7.07
C)​18.38
D)​10
E)​9.06

Question 61

Write the standard form of the equation of the circle with center (3,-2)and solution point (-2,3). ?

A) $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 50$
B) $( x - 3 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = \sqrt { 50 }$
C) $( x - 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 50$
D) $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = \sqrt { 50 }$
E) $( x - 3 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 50$

Question 62

Write the standard form of the equation of the circle with center (5,-7)and radius 5. ?

A)? $( x + 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 5$
B) $( x - 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 5$
C) $( x - 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$
D) $( x + 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$
E) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

Question 63

Write the standard form of the equation of the circle which has (-5,4)and (-1,8)as endpoints of a diameter. ?

A)? $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = \sqrt { 8 }$
B) $( x - 3 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$
C) $( x - 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$
D) $( x - 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = \sqrt { 8 }$
E) $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$

Question 64

The point A has coordinates (-3,5).If A is moved 3 units upward 6 units to the left,what are the new coordinates of A ? ​

A)(0,-1)
B)(3,8)
C)(0,11)
D)(-9,8)
E)(3,2)

Question 65

Let M denote the midpoint of the line segment joining (4,3)and (11,6).Find the distance from M to the point (-6,-5).Round the answer to the nearest tenth. ​

A)16.7
B)16.1
C)16.5
D)15.9
E)16.2

Question 66

Let M denote the midpoint of the line segment joining (2,3)and (7,6).Find the midpoint between M and (-6,-4). ​

A)(2,0.25)
B)(-0.75,0.25)
C)(-2,-0.5)
D)(4.5,4.5)
E)(0.5,1)

Question 67

Write the standard form of the equation of the circle tangent to the y-axis and with center (-3,-6). ?

A)? $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 9$
B) $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 3$
C) $( x - 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 9$
D) $( x + 3 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 3$
E) $( x + 3 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 9$

Question 68

Find the center and radius of the circle with equation $( x + 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$ . ?

A)Center: (7,2) Radius: 5
B)Center: (-7,2) Radius: 25
C)Center: (7,-2) Radius: 25
D)Center: (7,-2) Radius: 5
E)Center: (-7,2) Radius: 5

Question 69

Let S represent the midpoint between (5,3)and (-5,-7).Let T represent the midpoint between (5,3)and S.Find the coordinates of T. ​

A)(-2.5,-4.5)
B)(0,-2)
C)(0,0.5)
D)(2.5,0.5)
E)(2.5,-2)