Problem 1

An ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the _____ plane.

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Problem 2

The point of intersection of the $x$ - and $y$ -axes is the_____, and the two axes divide the coordinate plane into four parts called _____.

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Problem 4

Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the_____ ______.

Suzana M.

Numerade Educator

Problem 5

Plotting Points in the Cartesian Plane In

Exercises 5, plot the points in the Cartesian plane.

$$

(-4,2),(-3,-6),(0,5),(1,-4),(0,0),(3,1)

$$

Jimmy Y.

Numerade Educator

Problem 6

Plotting Points in the Cartesian Plane In

Exercises 6, plot the points in the Cartesian plane.

$$

\left(1,-\frac{1}{3}\right),(0.5,-1),\left(\frac{3}{7}, 3\right),\left(-\frac{4}{3},-\frac{3}{7}\right),(-2,2.5)

$$

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Problem 7

Finding the Coordinates of a Point In Exercises 7 and 8 , find the coordinates of the point. The point is located three units to the left of the $y$ -axis and four units above the $x$ -axis.

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Problem 8

Finding the Coordinates of a Point In Exercises 8, find the coordinates of the point. The point is on the $x$ -axis and 12 units to the left of the $y$ -axis.

Karuna R.

Numerade Educator

Problem 10

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is

located so that the condition(s) is (are) satisfied.

$$

x<0 \text { and } y<0

$$

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Problem 11

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is

located so that the condition(s) is (are) satisfied.

$$

x=-4 \text { and } y>0

$$

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Problem 12

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is

located so that the condition(s) is (are) satisfied.

$$

y<-5

$$

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Problem 13

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is

located so that the condition(s) is (are) satisfied.

$$

x<0 \text { and }-y>0

$$

Pranati M.

Numerade Educator

Problem 14

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is

located so that the condition(s) is (are) satisfied.

$$

x y>0

$$

Taylor S.

Numerade Educator

Problem 15

Sketching a Scatter Plot In Exercises 15 and $16,$ 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 2003 through $2010 .$ (Source: Wal-Mart Stores, Inc.)

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Problem 16

Sketching a Scatter Plot, 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 January. (Source: NOAA $)$

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Problem 17

Finding a Distance In Exercises $17-22,$ find the distance between the points.

$$(-2,6),(3,-6)$$

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Problem 18

Finding a Distance, find the distance between the points.

$$

(8,5),(0,20)

$$

Aryan N.

Numerade Educator

Problem 19

Finding a Distance, find the distance between the points.

$$

(1,4),(-5,-1)

$$

Yoochan S.

Numerade Educator

Problem 20

Finding a Distance, find the distance between the points.

$$

(1,3),(3,-2)

$$

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Problem 21

Finding a Distance, find the distance between the points.

$$

\left(\frac{1}{2}, \frac{4}{3}\right),(2,-1)

$$

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Problem 22

Finding a Distance, find the distance between the points.

$$

(9.5,-2.6),(-3.9,8.2)

$$

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Problem 23

Verifying a Right Triangle In Exercises 23,

(a) find the length of each side of the right triangle, and

(b) show that these lengths satisfy the Pythagorean Theorem.

Yitzchak S.

Numerade Educator

Problem 24

Verifying a Right Triangle In Exercises 24,

(a) find the length of each side of the right triangle, and

(b) show that these lengths satisfy the Pythagorean

Theorem.

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Problem 25

Verifying a Polygon, show that the points form the vertices of the indicated polygon. Right triangle: $(4,0),(2,1),(-1,-5)$

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Problem 26

Verifying a Polygon, show that the points form the vertices of the indicated polygon. Right triangle: $(-1,3),(3,5),(5,1)$

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Problem 27

Verifying a Polygon, show that

the points form the vertices of the indicated polygon.

Isosceles triangle: $(1,-3),(3,2),(-2,4)$

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Problem 28

Verifying a Polygon, show that

the points form the vertices of the indicated polygon.

Isosceles triangle: $(2,3),(4,9),(-2,7)$

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Problem 29

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

(6,-3),(6,5)

$$

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Problem 30

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

(1,4),(8,4)

$$

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Problem 31

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

(1,1),(9,7)

$$

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Problem 32

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

(1,12),(6,0)

$$

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Problem 33

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

(-1,2),(5,4)

$$

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Problem 34

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

(2,10),(10,2)

$$

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Problem 35

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

(-16.8,12.3),(5.6,4.9)

$$

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Problem 36

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between

the points, and (c) find the midpoint of the line

segment joining the points.

$$

\left(\frac{1}{2}, 1\right),\left(-\frac{5}{2}, \frac{4}{3}\right)

$$

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Problem 37

An airplane flies from

Naples, Italy, in a

straight line to Rome,

Italy, which is

120 kilometers north

and 150 kilometers

west of Naples. How

far does the plane fly?

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Problem 38

Sports A soccer player passes the ball from a point

that is 18 yards from the endline and 12 yards from the

sideline. A teammate who is 42 yards from the same

endline and 50 yards from the same sideline receives

the pass. (See figure.) How long is the pass?

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Problem 39

Sales The Coca-Cola Company had sales of $\$ 19,564$

million in 2002 and $\$ 35,123$ million in $2010 .$ Use the

Midpoint Formula to estimate the sales in $2006 .$

Assume that the sales followed a linear pattern.

(Source: The Coca-Cola Company)

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Problem 40

Earnings per Share The earnings per share for

Big Lots, Inc. were $\$ 1.89$ in 2008 and $\$ 2.83$ in $2010 .$

Use the Midpoint Formula to estimate the earnings

per share in $2009 .$ Assume that the earnings per share

followed a linear pattern. (Source: Big Lots, Inc.)

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Problem 41

Translating Points in the Plane In Exercises 41,

find the coordinates of the vertices of the polygon after

the indicated translation to a new position in the plane.

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Problem 42

Translating Points in the Plane In Exercises 42,

find the coordinates of the vertices of the polygon after

the indicated translation to a new position in the plane.

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Problem 43

Translating Points in the Plane,

find the coordinates of the vertices of the polygon after

the indicated translation to a new position in the plane.

Original coordinates of vertices: $(-7,-2),(-2,2),$

$(-2,-4),(-7,-4)$

Shift: eight units up, four units to the right

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Problem 44

Translating Points in the Plane,

find the coordinates of the vertices of the polygon after

the indicated translation to a new position in the plane.

Original coordinates of vertices: $(5,8),(3,6),(7,6)$

Shift: 6 units down, 10 units to the left

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Problem 45

Minimum Wage Use the graph below, which

shows the minimum wages in the United States (in

dollars) from 1950 through $2011 .$ (Source: U.S.

Department of Labor)

(a) Which decade shows the greatest increase in

minimum wage?

(b) Approximate the percent increases in the minimum

wage from 1990 to 1995 and from 1995 to 2011 .

(c) Use the percent increase from 1995 to 2011 to

predict the minimum wage in $2016 .$

(d) Do you believe that your prediction in part (c) is

reasonable? Explain.

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Problem 46

Data Analysis: Exam Scores The table shows

the mathematics entrance test scores $x$ and the final

examination scores $y$ in an algebra course for a sample

of 10 students.

$$

\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline x & {22} & {29} & {35} & {44} & {48} & {53} & {58} & {65} & {76} \\ \hline y & {53} & {74} & {57} & {66} & {79} & {90} & {76} & {93} & {99} \\ \hline\end{array}

$$

(a) Sketch a scatter plot of the data.

(b) Find the entrance test score of any student with a

final exam score in the 80s.

(c) Does a higher entrance test score imply a higher

final exam score? Explain.

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Problem 47

Using the Midpoint Formula A line segment.

has $\left(x_{1}, y_{1}\right)$ as one endpoint and $\left(x_{m}, y_{m}\right)$ as its midpoint.

Find the other endpoint $\left(x_{2}, y_{2}\right)$ of the line segment in

terms of $x_{1}, y_{1}, x_{m}$ , and $y_{n m}$

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Problem 48

Using the Midpoint Formula Use the result of

Exercise 47 to find the coordinates of the endpoint of a

line segment when the coordinates of the other endpoint

and midpoint are, respectively,

$$

\text { (a) }(1,-2),(4,-1) \text { and }\text { (b) }(-5,11),(2,4)

$$

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Problem 49

Using the Midpoint Formula Use the Midpoint

Formula three times to find the three points that divide

the line segment joining $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ into four

parts.

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Problem 50

Using the Midpoint Formula Use the result

of Exercise 49 to find the points that divide the line

segment joining the given points into four equal parts.

$$

(\mathrm{a})(1,-2),(4,-1) \quad \text { (b) }(-2,-3),(0,0)

$$

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Problem 51

Make a Conjecture Plot the points $(2,1),(-3,5),$

and $(7,-3)$ on a rectangular coordinate system. Then

change the signs of the indicated coordinates of each

point and plot the three new points on the same

rectangular coordinate system. Make a conjecture about

the location of a point when each of the following

occurs.

(a) The sign of the $x$ -coordinate is changed.

(b) The sign of the $y$ -coordinate is changed.

(c) The signs of both the $x$ - and $y$ -coordinates are

changed.

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Problem 52

Collinear Points Three or more points are

collinear when they all lie on the same line. Use the

steps following to determine whether the set of points

$\{A(2,3), B(2,6), C(6,3)\}$ and the set of points $\{A(8,3),$

$B(5,2), C(2,1) \}$ are collinear.

(a) For each set of points, use the Distance Formula to

find the distances from $A$ to $B,$ from $B$ to $C,$ and

from $A$ to $C .$ What relationship exists among these

distances for each set of points?

(b) Plot each set of points in the Cartesian plane. Do all

the points of either set appear to lie on the same

line?

(c) Compare your conclusions from part (a) with the

conclusions you made from the graphs in part (b).

Make a general statement about how to use the

Distance Formula to determine collinearity.

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Problem 53

Think About It When plotting points on the

rectangular coordinate system, is it true that the scales

on the $x-$ and $y$ -axes must be the same? Explain.

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Problem 54

Think About It What is the $y$ -coordinate of any

point on the $x$ -axis? What is the $x$ -coordinate of any

point on the $y$ -axis?

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Problem 55

True or False? , determine whether

the statement is true or false. Justify your answer.

In order to divide a line segment into 16 equal parts, you

would have to use the Midpoint Formula 16 times.

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Problem 56

True or False? , determine whether

the statement is true or false. Justify your answer.

The points $(-8,4),(2,11),$ and $(-5,1)$ represent the

vertices of an isosceles triangle.

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Problem 57

True or False? , determine whether

the statement is true or false. Justify your answer.

If four points represent the vertices of a polygon, and

the four sides are equal, then the polygon must be a

square.

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Problem 58

HOW DOYOU SEE IT? Use the plot of

the point $\left(x_{0}, y_{0}\right)$ in the figure. Match the

transformation of the point with the correct

plot. Explain your reasoning. IThe plots are

labeled (i), (ii), (iii), and (iv).]

$$

\begin{array}{ll}{\text { (a) }\left(x_{0}, y_{0}\right)} & {\text { (b) }\left(-2 x_{0}, y_{0}\right)} \\ {\text { (c) }\left(x_{0}, \frac{1}{2} y_{0}\right)} & {\text { (d) }\left(-x_{0},-y_{0}\right)}\end{array}

$$

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Problem 59

Proof Prove that the diagonals of the parallelogram

in the figure intersect at their midpoints.

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