Collinear Points Three or more points are collinear if they all lie on the same line

Match each term with its definition. (a) -axis (i) point of intersection of vertical axis and horizontal axis (b) -axis (ii) directed distance from the x-axis (c) origin (iii) directed distance from the y-axis (d) quadrants (iv) four regions of the coordinate plane (e) -coordinate (v) horizontal real number line (f ) -coordinate (vi) vertical real number line

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

The ________ ________ is a result derived from the Pythagorean Theorem.

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 ________ ________.

In Exercises 36, plot the points in the Cartesian plane.

In Exercises 36, plot the points in the Cartesian plane.

The point is located three units to the left of the -axis and four units above the -axis.

The point is located eight units below the -axis and four units to the right of the -axis.

The point is located five units below the -axis and the coordinates of the point are equal.

The point is on the -axis and 12 units to the left of the -axis. xy

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

In Exercises 1120, determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

Number of Stores The table shows the number of Wal-Mart stores for each year from 1996 through 2003. (Source: Wal-Mart Stores, Inc.)

Meteorology The table shows the lowest temperature on record (in degrees Fahrenheit) in Duluth, Minnesota for each month where represents January. (Source: NOAA) Note:

In Exercises 2326, find the distance between the points. (Note: In each case, the two points lie on the same horizontal or vertical line.)

In Exercises 2326, find the distance between the points. (Note: In each case, the two points lie on the same horizontal or vertical line.)

In Exercises 2326, find the distance between the points. (Note: In each case, the two points lie on the same horizontal or vertical line.)

In Exercises 2326, find the distance between the points. (Note: In each case, the two points lie on the same horizontal or vertical line.)

In Exercises 2730, (a) find the length of each side of the right triangle, and (b) show that these lengths satisfy the Pythagorean Theorem.

In Exercises 2730, (a) find the length of each side of the right triangle, and (b) show that these lengths satisfy the Pythagorean Theorem.

In Exercises 2730, (a) find the length of each side of the right triangle, and (b) show that these lengths satisfy the Pythagorean Theorem.

In Exercises 2730, (a) find the length of each side of the right triangle, and (b) show that these lengths satisfy the Pythagorean Theorem.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 3140, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.

In Exercises 41 and 42, show that the points form the vertices of the indicated polygon. Right triangle:

In Exercises 41 and 42, show that the points form the vertices of the indicated polygon. Isosceles triangle:

A line segment has as one endpoint and as its midpoint. Find the other endpoint of the line segment in terms of and

Use the result of Exercise 43 to find the coordinates of the endpoint of a line segment if the coordinates of the other endpoint and midpoint are, respectively, (a) and (b)

Use the Midpoint Formula three times to find the three points that divide the line segment joining and into four parts.

Use the result of Exercise 45 to find the points that divide the line segment joining the given points into four equal parts. (a) (b)

Sports A soccer player passes the ball from a point that is 18 yards from the endline and 12 yards from the sideline. The pass is received by a teammate who is 42 yards from the same endline and 50 yards from the same sideline, as shown in the figure. How long is the pass?

Flying Distance 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?

In Exercises 49 and 50, use the Midpoint Formula to estimate the sales of Big Lots, Inc. and Dollar Tree Stores, Inc. in 2002, given the sales in 2001 and 2003. Assume that the sales followed a linear pattern. (Source: Big Lots, Inc.; Dollar Tree Stores, Inc.)Big Lots

In Exercises 49 and 50, use the Midpoint Formula to estimate the sales of Big Lots, Inc. and Dollar Tree Stores, Inc. in 2002, given the sales in 2001 and 2003. Assume that the sales followed a linear pattern. (Source: Big Lots, Inc.; Dollar Tree Stores, Inc.)Dollar Tree

In Exercises 5154, the polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position.

In Exercises 5154, the polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position.

In Exercises 5154, the polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position.Original coordinates of vertices: Shift: eight units upward, four units to the right

In Exercises 5154, the polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position.Original coordinates of vertices: Shift: 6 units downward, 10 units to the left Retail Price (Source: U.S. Bureau of Labor Statistics)

Approximate the highest price of a pound of butter shown in the graph. When did this occur?

Approximate the percent change in the price of butter from the price in 1995 to the highest price shown in the graph. Advertising (Source: USA Today Research and CNN)

Approximate the percent increase in the cost of a 30-second spot from Super Bowl XXIII in 1989 to Super Bowl XXXV in 2001.

Estimate the percent increase in the cost of a 30-second spot (a) from Super Bowl XXIII in 1989 to Super Bowl XXVII in 1993 and (b) from Super Bowl XXVII in 1993 to Super Bowl XXXVII in 2003.

Music The graph shows the numbers of recording artists who were elected to the Rock and Roll Hall of Fame from 1986 to 2004. (a) Describe any trends in the data. From these trends, predict the number of artists elected in 2008. (b) Why do you think the numbers elected in 1986 and 1987 were greater in other years?

Labor Force Use the graph below, which shows the minimum wage in the United States (in dollars) from 1950 to 2004. (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 2004. (c) Use the percent increase from 1995 to 2004 to predict the minimum wage in 2008. (d) Do you believe that your prediction in part (c) is reasonable? Explain.

Sales The Coca-Cola Company had sales of $18,546 million in 1996 and $21,900 million in 2004. Use the Midpoint Formula to estimate the sales in 1998, 2000, and 2002. Assume that the sales followed a linear pattern. (Source: The Coca-Cola Company)

Data Analysis: Exam Scores The table shows the mathematics entrance test scores and the final examination scores in an algebra course for a sample of 10 students. (a) Sketch a scatter plot of the data. (b) Find the entrance exam score of any student with a final exam score in the 80s. (c) Does a higher entrance exam score imply a higher final exam score? Explain.

Volume of a Billiard Ball A billiard ball has a volume of 5.96 cubic inches. Find the radius of a billiard ball.

Length of a Tank The diameter of a cylindrical propane gas tank is 4 feet. The total volume of the tank is 603.2 cubic feet. Find the length of the tank.

Geometry A Slow Moving Vehicle sign has the shape of an equilateral triangle. The sign has a perimeter of 129 centimeters. Find the length of each side of the sign. Find the area of the sign.

Geometry The radius of a traffic cone is 14 centimeters and the lateral surface of the cone is 1617 square centimeters. Find the height of the cone.

Dimensions of a Room A room is 1.5 times as long as it is wide, and its perimeter is 25 meters. (a) Draw a diagram that represents the problem. Identify the length as and the width as (b) Write in terms of and write an equation for the perimeter in terms of (c) Find the dimensions of the room.

Dimensions of a Container The width of a rectangular storage container is 1.25 times its height. The length of the container is 16 inches and the volume of the container is 2000 cubic inches. (a) Draw a diagram that represents the problem. Label the height, width, and length accordingly. (b) Write in terms of and write an equation for the volume in terms of (c) Find the dimensions of the container.

Data Analysis: Mail The table shows the number of pieces of mail handled (in billions) by the U.S. Postal Service for each year from 1996 through 2003. (Source: U.S. Postal Service) (a) Sketch a scatter plot of the data. (b) Approximate the year in which there was the greatest decrease in the number of pieces of mail handled. (c) Why do you think the number of pieces of mail handled decreased?

Data Analysis: Athletics The table shows the numbers of mens M and womens W college basketball teams for each year from 1994 through 2003. (Source: National Collegiate Athletic Association) (a) Sketch scatter plots of these two sets of data on the same set of coordinate axes. (b) Find the year in which the numbers of mens and womens teams were nearly equal. (c) Find the year in which the difference between the numbers of mens and womens teams was the greatest. What was this difference?

Make a Conjecture Plot the points and on a rectangular coordinate system. Then change the sign of the -coordinate 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 -coordinate is changed. (b) The sign of the -coordinate is changed. (c) The signs of both the - and -coordinates are changed.

Collinear Points Three or more points are collinear if they all lie on the same line. Use the steps below to determine if the set of points and the set of points are collinear. (a) For each set of points, use the Distance Formula to find the distances from to from to and from to 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. True or False?

In order to divide a line segment into 16 equal parts, you would have to use the Midpoint Formula 16 times.

The points and represent the vertices of an isosceles triangle.

Think About It When plotting points on the rectangular coordinate system, is it true that the scales on the - and -axes must be the same? Explain.

Proof Prove that the diagonals of the parallelogram in the figure intersect at their midpoints. FIGURE FOR 76 FIGURE FOR 7780 (a) (b) (c) (d)

In Exercises 7780, use the plot of the point in the figure. Match the transformation of the point with the correct plot. [The plots are labeled (a), (b), (c), and (d).]

In Exercises 7780, use the plot of the point in the figure. Match the transformation of the point with the correct plot. [The plots are labeled (a), (b), (c), and (d).]

In Exercises 7780, use the plot of the point in the figure. Match the transformation of the point with the correct plot. [The plots are labeled (a), (b), (c), and (d).]

In Exercises 7780, use the plot of the point in the figure. Match the transformation of the point with the correct plot. [The plots are labeled (a), (b), (c), and (d).]

In Exercises 8188, solve the equation or inequality.

In Exercises 8188, solve the equation or inequality.

In Exercises 8188, solve the equation or inequality.

In Exercises 8188, solve the equation or inequality.

In Exercises 8188, solve the equation or inequality.

In Exercises 8188, solve the equation or inequality.

In Exercises 8188, solve the equation or inequality._x _ 18_ < 4

In Exercises 8188, solve the equation or inequality._2x _ 15_ 11