35 R.3 Real Number Operations and Properties Distance between Points on a Number Line If P and Q are points on a number line with coordinates a and b, respectively, then the distance d1P, Q2 between them is given by the following. d1P, Q2 = 0 b −a0 or d1P, Q2 = 0 a −b0 That is, the distance between two points on a number line is the absolute value of the difference between their coordinates in either order. See Figure 19. EXAMPLE 11 Finding the Distance betweenTwo Points Find the distance between -5 and 8. SOLUTION Use the first formula in the preceding box, with a = -5 and b = 8. d1P, Q2 = 0 b - a0 = 0 8 - 1-52 0 = 0 8 + 50 = 0 130 = 13 Using the second formula in the box, we obtain the same result. d1P, Q2 = 0 a - b0 = 0 1-52 - 8 0 = 0 -130 = 13 S Now Try Exercise 151. R.3 Exercises CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. 1. If the real number a is to the left of the real number b on a number line, then a b. 2. The distance on a number line from a number to 0 is the of that number. 3. The sum of two negative numbers is . 4. The product of two negative numbers is . 5. In the expression 63, 6 is the , and 3 is the . CONCEPT PREVIEW Evaluate each expression. 6. 0 7 7. 10 3 8. 2 # 5 - 10 , 2 9. 0 -40 10. CONCEPT PREVIEW Rewrite the expression -71x - 4y2 using the distributive property. Evaluate each expression. See Example 1. 11. 0 -100 12. 0 -150 13. - ` 4 7 ` 14. - ` 7 2 ` 15. -0 -30 16. -0 -120 Determine whether each statement is true or false. 17. 0 250 = 0 -250 18. 0 -80 Ú 0 19. 0 5 + 1-132 0 = 0 50 + 0 -130 20. 0 8 - 120 = 0 80 - 0 120 21. 0 110 # 0 -60 = 0 -660 22. 0 -50 # 0 60 = 0 -5 # 60 P a Q b d(P, Q) Figure 19
RkJQdWJsaXNoZXIy NjM5ODQ=