1. Copyright © 2011 Pearson, Inc. 8.6 Three- Dimensional Cartesian Coordinate System

2. Copyright © 2011 Pearson, Inc. Slide 8.6 - 2 What you’ll learn about Three-Dimensional Cartesian Coordinates Distances and Midpoint Formula Equation of a Sphere Planes and Other Surfaces Vectors in Space Lines in Space … and why This is the analytic geometry of our physical world.

3. Copyright © 2011 Pearson, Inc. Slide 8.6 - 3 The Point P(x,y,z) in Cartesian Space

4. Copyright © 2011 Pearson, Inc. Slide 8.6 - 4 The Coordinate Planes Divide Space into Eight Octants

5. Copyright © 2011 Pearson, Inc. Slide 8.6 - 5 Distance Formula (Cartesian Space)

6. Copyright © 2011 Pearson, Inc. Slide 8.6 - 6 Midpoint Formula (Cartesian Space)

7. Copyright © 2011 Pearson, Inc. Slide 8.6 - 7 Example Calculating a Distance and Finding a Midpoint

8. Copyright © 2011 Pearson, Inc. Slide 8.6 - 8 Example Calculating a Distance and Finding a Midpoint

9. Copyright © 2011 Pearson, Inc. Slide 8.6 - 9 Drawing Lesson

10. Copyright © 2011 Pearson, Inc. Slide 8.6 - 10 Drawing Lesson (cont’d)

11. Copyright © 2011 Pearson, Inc. Slide 8.6 - 11 Standard Equation of a Sphere

12. Copyright © 2011 Pearson, Inc. Slide 8.6 - 12 Example Finding the Standard Equation of a Sphere

13. Copyright © 2011 Pearson, Inc. Slide 8.6 - 13 Example Finding the Standard Equation of a Sphere

14. Copyright © 2011 Pearson, Inc. Slide 8.6 - 14 Equation for a Plane in Cartesian Space

15. Copyright © 2011 Pearson, Inc. Slide 8.6 - 15 The Vector v =

16. Copyright © 2011 Pearson, Inc. Slide 8.6 - 16 Vector Relationships in Space

17. Copyright © 2011 Pearson, Inc. Slide 8.6 - 17 Equations for a Line in Space

18. Copyright © 2011 Pearson, Inc. Slide 8.6 - 18 Example Finding Equations for a Line

19. Copyright © 2011 Pearson, Inc. Slide 8.6 - 19 Example Finding Equations for a Line

20. Copyright © 2011 Pearson, Inc. Slide 8.6 - 20 Quick Review

21. Copyright © 2011 Pearson, Inc. Slide 8.6 - 21 Quick Review Solutions

22. Copyright © 2011 Pearson, Inc. Slide 8.6 - 22 Chapter Test

23. Copyright © 2011 Pearson, Inc. Slide 8.6 - 23 Chapter Test

24. Copyright © 2011 Pearson, Inc. Slide 8.6 - 24 Chapter Test

25. Copyright © 2011 Pearson, Inc. Slide 8.6 - 25 Chapter Test Solutions

26. Copyright © 2011 Pearson, Inc. Slide 8.6 - 26 Chapter Test Solutions

27. Copyright © 2011 Pearson, Inc. Slide 8.6 - 27 Chapter Test Solutions

28. Copyright © 2011 Pearson, Inc. Slide 8.6 - 28 Chapter Test Solutions