9. The name of the red pt. is ___ The coordinate of the red pt. is ___ The name of the grey pt. is ___ The coordinate of the grey pt. is __ E 0 J 5
10.
11. Calculation of Distance Using Coordinates 3 5 You could simply count the blocks. The answer is 2.
12. Calculation of Distance Using Coordinates 3 33 Counting blocks would be time consuming. The answer is 30. You could simply subtract. Subtraction means the difference between numbers.
13. Calculation of Distance Using Coordinates -8 33 The answer is 41. You could simply subtract. 33 – (-8) = 33 + 8 = 41 Note that negative numbers requires using algebra.
14. -8 -5 You could simply subtract. -5 – (-8) = -5 + 8 = 3 However if we subtract the numbers in reverse, then... -8 – (-5) = -8 + 5 = - 3 Therefore to avoid negative numbers, we take the absolute value of the differences.
15. a b You subtract the coordinates then take the absolute value of the difference. Distance =
16. 1 3 4 4 1 5 9 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 1
17. 1 2 3 4 4 1 5 9 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 2
18. 1 2 3 3 4 4 1 5 9 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 3
19. 1 2 3 3 1 5 9 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 3
20. 1 2 3 4 4 1 5 9 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 3
21. 1 2 3 4 4 4 1 5 9 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 3
22. 1 2 3 3 4 4 1 5 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 5
23. 1 2 3 3 4 4 1 5 9 Method 1: Count the blocks. Method 2: Subtract coordinates and take the absolute value. 9
24.
25. If M is on the segment and M is a midpoint of It is necessary for both conditions. Let’s see why?
26. D, E, and F Are equidistant from both A and B But they are NOT midpoints. The midpoint Must be on the Segment !
27. Bisectors Bisectors can be any segment, ray, line, or plane if they go thru the midpoint of a segment.
28. D is midpoint of E is midpoint of C is midpoint of B is midpoint of Find the value of their coordinates.
36. Segment Addition Postulate A B C If B is between A and C, then…. AB + BC = AC Note: Between means that A, B, and C are collinear. B must be on the segment AC.
37. Segment Addition Postulate Applications A B C 22 AB = 8 BC = 22 AC = ? 8 First, label the diagram. x Second, find equation. Third, solve equation. 8 + 22 = x 30 = x
38. Segment Addition Postulate Applications A B C 22 AB = 8 AC = 22 BC = ? 8 First, label the diagram. x Second, find equation. Third, solve equation. 8 + x = 22 x = 14
39. Segment Addition Postulate Applications A B C 18 AB = 3x - 4 BC = 2x + 7 AC = 18 Find AB & BC 3x - 4 First, label the diagram. 2x + 7 Second, find equation. Third, solve equation. 3x- 4 + 2x + 7 = 18 5x + 3 = 18 5x = 15 x = 3 Not done yet?
40. Segment Addition Postulate Applications A B C 18 AB = 3x - 4 BC = 2x + 7 AC = 18 Find AB & BC 3x - 4 2x + 7 3x- 4 + 2x + 7 = 18 5x + 3 = 18 5x = 15 x = 3 Substitute Back in. 3x - 4 3(3) - 4 9- 4 = 5 2x + 7 2(3) + 7 6 + 7 = 13 13 5
41. Segment Addition Postulate Applications A B C 16 AB = 3x - 13 BC = 16 AC = 4x + 14 Find AB & AC 3x - 13 4x - 4 3x- 13 + 16 = 4x - 4 - x = - 7 Label diagram. Find equation. Solve equation. 3x+3 = 4x - 4 x = 7 Not Done Yet NDY
42. Segment Addition Postulate Applications A B C 16 AB = 3x - 13 BC = 16 AC = 4x + 14 Find AB & AC 3x - 13 4x - 4 3x- 13 + 16 = 4x - 4 - x = - 7 Substitute into expressions. 3x+3 = 4x - 4 x = 7 3x - 13 3(7) - 13 21 - 13 8 8 4(7) - 14 4x - 14 28 - 14 24 24
43. You must be able to do these complex algebraic problems. They will be in the chapter test and the marking period exam (QPA)
44. Summary A B There are several symbols for geometric terms. C D F E B C No symbol means… The distance from B to C. A numerical value.
45. Summary 2 A B There are alternate symbols for distance, length, or measurement. 5 5 Measurements are always arbitrary due to the choice of units (meters, feet, etc.), degree of accuracy and scale.
46. Summary 3 The letters are the names of the points. The numbers are the coordinates that indicate the relative position of each point.
47. Summary 4 The ruler postulate allows us to… 1. Build number lines at any scale. 2. Compute distance by taking the absolute value of the difference of the coordinates.
48. Summary 5 The segment addition postulate allows us to conclude… The distance on a line is the sum of its parts. A B C AB + BC = AC
49. Summary 6 A B C 18 AB = 3x - 4 BC = 2x + 7 AC = 18 Find AB & BC 3x - 4 2x + 7 You must be able to do these algebraic problems.