In Exercises 58, evaluate the expression.2 - -2

In Exercises 1 and 2, plot the two numbers on a number line. Then find the distance between them. \(\sqrt{7},\ \sqrt{2}\)

In Exercises 1 and 2, plot the two numbers on a number line. Then find the distance between them. \(-\frac{5}{3},\ -\frac{9}{5}\)

In Exercises 3 and 4, plot the real numbers on a number line. -3, 4, 2.5, 0, -1.5

In Exercises 3 and 4, plot the real numbers on a number line. \(-\frac{5}{2},\ -\frac{1}{2},\ \frac{2}{3},\ 0,\ -1\)

In Exercises 5 and 6, plot the points. A(3, 5), B(-2, 4), C(3, 0), D(0, -3)

In Exercises 5 and 6, plot the points. A(-3, -5), B(2, -4), C(0, 5), D(-4, 0)

In Exercises 7–10, use a calculator to evaluate the expression. Round your answer to two decimal places. \(\frac{-17+28}{2}\)

In Exercises 7–10, use a calculator to evaluate the expression. Round your answer to two decimal places. \(\sqrt{13^2 + 17^2}\)

In Exercises 7–10, use a calculator to evaluate the expression. Round your answer to two decimal places. \(\sqrt{6^2 + 8^2}\)

In Exercises 7–10, use a calculator to evaluate the expression. Round your answer to two decimal places. \(\sqrt{(17-3)^2 + (-4 - 8)^2}\)

In Exercises 1 and 2, estimate the coordinates of the points.

In Exercises 1 and 2, estimate the coordinates of the points.

In Exercises 3 and 4, name the quadrants containing the points. (a) (2, 4) (b) (0, 3) (c) (-2, 3) (d) (-1, -4)

In Exercises 3 and 4, name the quadrants containing the points. (a) \((\frac{1}{2},\ \frac{3}{2})\) (b) (-2, 0) (c) (-1, -2) (d) \((-\frac{3}{2},\ -\frac{7}{3})\)

In Exercises 5–8, evaluate the expression. 3 + |-3|

In Exercises 5–8, evaluate the expression. 2 - |-2|

In Exercises 5–8, evaluate the expression. |(-2)3|

In Exercises 5–8, evaluate the expression. \(\frac{-2}{|-2|}\)

In Exercises 9 and 10, rewrite the expression without using absolute value symbols. \(| \pi - 4 |\)

In Exercises 9 and 10, rewrite the expression without using absolute value symbols. \(| \sqrt{5} - 5/2 |\)

In Exercises 11–18, find the distance between the points. -9.3, 10.6

In Exercises 11–18, find the distance between the points. -5, -17

In Exercises 11–18, find the distance between the points. (-3, -1), (5, -1)

In Exercises 11–18, find the distance between the points. (-4, -3), (1, 1)

In Exercises 11–18, find the distance between the points. (0, 0), (3, 4)

In Exercises 11–18, find the distance between the points. (-1, 2), (2, -3)

In Exercises 11–18, find the distance between the points. (-2, 0), (5, 0)

In Exercises 11–18, find the distance between the points. (0, -8), (0, -1)

In Exercises 19–22, find the area and perimeter of the figure determined by the points. (-5, 3), (0, -1), (4, 4)

In Exercises 19–22, find the area and perimeter of the figure determined by the points. (-2, -2), (-2, 2), (2, 2), (2, -2)

In Exercises 19–22, find the area and perimeter of the figure determined by the points. (-3, -1), (-1, 3), (7, 3), (5, -1)

In Exercises 19–22, find the area and perimeter of the figure determined by the points. (-2, 1), (-2, 6), (4, 6), (4, 1)

In Exercises 23–28, find the midpoint of the line segment with the given endpoints. -9.3, 10.6

In Exercises 23–28, find the midpoint of the line segment with the given endpoints. -5, -17

In Exercises 23–28, find the midpoint of the line segment with the given endpoints. (-1, 3), (5, 9)

In Exercises 23–28, find the midpoint of the line segment with the given endpoints. \((3, \sqrt{2}),\ (6,\ 2)\)

In Exercises 23–28, find the midpoint of the line segment with the given endpoints. (-7/3, 3/4), (5/3, -9/4)

In Exercises 23–28, find the midpoint of the line segment with the given endpoints. (5, -2), (-1, -4)

In Exercises 29–34, draw a scatter plot of the data given in the table. U.S. Motor Vehicle Production The total number of motor vehicles in thousands (y) produced by the United States each year from 2001 to 2007 is given in the table. (Source: Automotive News Data Center and R. L. Polk Marketing Systems as reported in The World Almanac and Book of Facts 2009.)

In Exercises 29–34, draw a scatter plot of the data given in the table. World Motor Vehicle Production The total number of motor vehicles in thousands (y) produced in the world each year from 2001 to 2007 is given in the table. (Source: American Automobile Manufacturers Association as reported in The World Almanac and Book of Facts 2009.)

In Exercises 29–34, draw a scatter plot of the data given in the table. U.S. Imports from Mexico The total in billions of dollars of U.S. imports from Mexico from 2000 to 2007 is given in Table P.3.

In Exercises 29–34, draw a scatter plot of the data given in the table. U.S. Agricultural Exports The total in billions of dollars of U.S. agricultural exports from 2000 to 2007 is given in Table P.4.

In Exercises 29–34, draw a scatter plot of the data given in the table. U.S. Agricultural Trade Surplus The total in billions of dollars of U.S. agricultural trade surplus from 2000 to 2007 is given in Table P.5.

In Exercises 29–34, draw a scatter plot of the data given in the table. U.S. Exports to Canada The total in billions of dollars of U.S. exports to Canada from 2000 to 2007 is given in Table P.6.

In Exercises 35 and 36, use the graph of the investment value of a $10,000 investment made in 1978 in Fundamental Investors™ of the American Funds™. The value as of January is shown for a few recent years in the graph below. (Source: Annual report of Fundamental Investors for the year ending December 31, 2004.) Reading from Graphs Use the graph to estimate the value of the investment as of (a) January 1997 and (b) January 2000.

In Exercises 35 and 36, use the graph of the investment value of a $10,000 investment made in 1978 in Fundamental Investors™ of the American Funds™. The value as of January is shown for a few recent years in the graph below. (Source: Annual report of Fundamental Investors for the year ending December 31, 2004.) 36. Percent Increase Estimate the percent increase in the value of the $10,000 investment from (a) January 1996 to January 1997. (b) January 2000 to January 2001. (c) January 1995 to January 2004.

Prove that the figure determined by the points is an isosceles triangle: (1, 3), (4, 7), (8, 4)

Group Activity Prove that the diagonals of the figure determined by the points bisect each other. (a) Square (-7, -1), (-2, 4), (3, -1), (-2, -6) (b) Parallelogram (-2, -3), (0, 1), (6, 7), (4, 3)

(a) Find the lengths of the sides of the triangle in the figure. (b) Writing to Learn Show that the triangle is a right triangle.

(a) Find the lengths of the sides of the triangle in the figure. (b) Writing to Learn Show that the triangle is a right triangle.

In Exercises 41–44, find the standard form equation for the circle. Center (1, 2), radius 5

In Exercises 41–44, find the standard form equation for the circle. Center (-3, 2), radius 1

In Exercises 41–44, find the standard form equation for the circle. Center (-1, -4), radius 3

In Exercises 41–44, find the standard form equation for the circle. Center (0, 0), radius \(\sqrt{3}\)

In Exercises 45–48, find the center and radius of the circle. \((x - 3)^2 + (y - 1)^2 = 36\)

In Exercises 45–48, find the center and radius of the circle. \((x + 4)^2 + (y - 2)^2 = 121\)

In Exercises 45–48, find the center and radius of the circle. \(x^2 + y^2 = 5\)

In Exercises 45–48, find the center and radius of the circle. \((x - 2)^2 + (y + 6)^2 = 25\)

In Exercises 49–52, write the statement using absolute value notation. The distance between x and 4 is 3.

In Exercises 49–52, write the statement using absolute value notation. The distance between y and -2 is greater than or equal to 4.

In Exercises 49–52, write the statement using absolute value notation. The distance between x and c is less than d units.

In Exercises 49–52, write the statement using absolute value notation. y is more than d units from c.

Determining a Line Segment with Given Midpoint Let (4, 4) be the midpoint of the line segment determined by the points (1, 2) and (a, b). Determine a and b.

Writing to Learn Isosceles but Not Equilateral Triangle Prove that the triangle determined by the points (3, 0), (-1, 2), and (5, 4) is isosceles but not equilateral.

Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the midpoint of the hypotenuse of the right triangle with vertices (0, 0), (5, 0), and (0, 7) is equidistant from the three vertices.

Writing to Learn Describe the set of real numbers that satisfy |x - 2| < 3.

Writing to Learn Describe the set of real numbers that satisfy \(|x + 3|\ \geq\ 5\).

True or False If a is a real number, then \(|a|\ \geq\ 0\). Justify your answer.

True or False Consider the right triangle ABC shown at the right. If M is the midpoint of the segment AB, then M’ is the midpoint of the segment AC. Justify your answer.

In Exercises 60–63, solve these problems without using a calculator. Multiple Choice Which of the following is equal to \(|1 - \sqrt{3}|\)? (A) \(1 - \sqrt{3}\) (B) \(\sqrt{3} - 1\) (C) \((1 - \sqrt{3})^2\) (D) \(\sqrt{2}\) (E) \(\sqrt{1/3}\)

Multiple Choice Which of the following is the midpoint of the line segment with endpoints -3 and 2? (A) 5/2 (B) 1 (C) -1/2 (D) -1 (E) -5/2

Which of the following is the center of the circle \((x - 3)^2 + (y + 4)^2 = 2\)? (A) (3, -4) (B) (-3, 4) (C) (4, -3) (D) (-4, 3) (E) (3/2, -2)

Multiple Choice Which of the following points is in the third quadrant? (A) (0, -3) (B) (-1, 0) (C) (2, -1) (D) (-1, 2) (E) (-2, -3)

Dividing a Line Segment into Thirds (a) Find the coordinates of the points one-third and two-thirds of the way from a = 2 to b = 8 on a number line. (b) Repeat (a) for a = -3 and b = 7. (c) Find the coordinates of the points one-third and two-thirds of the way from a to b on a number line. (d) Find the coordinates of the points one-third and two-thirds of the way from the point (1, 2) to the point (7, 11) in the coordinate plane. (e) Find the coordinates of the points one-third and two-thirds of the way from the point (a, b) to the point (c, d) in the coordinate plane.

Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the midpoint of the hypotenuse of any right triangle is equidistant from the three vertices.

Comparing Areas Consider the four points A(0, 0), B(0, a), C(a, a), and D(a, 0). Let P be the midpoint of the line segment CD and Q the point one-fourth of the way from A to D on segment AD. (a) Find the area of triangle BPQ. (b) Compare the area of triangle BPQ with the area of square ABCD.

In Exercises 67–69, let P(a, b) be a point in the first quadrant. Find the coordinates of the point Q in the fourth quadrant so that PQ is perpendicular to the x-axis.

In Exercises 67–69, let P(a, b) be a point in the first quadrant. Find the coordinates of the point Q in the second quadrant so that PQ is perpendicular to the y-axis.

In Exercises 67–69, let P(a, b) be a point in the first quadrant. Find the coordinates of the point Q in the third quadrant so that the origin is the midpoint of the segment PQ.

Writing to Learn Prove that the distance formula for the number line is a special case of the distance formula for the Cartesian plane.