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Foundations of Cartesian Coordinate Systems: Mastering Distance, Midpoint, and Equations

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  1. P.2 Cartesian Coordinate System

  2. What you’ll learn about • Cartesian Plane • Absolute Value of a Real Number • Distance Formulas • Midpoint Formulas • Equations of Circles • Applications … and why These topics provide the foundation for the material that will be covered in this textbook.

  3. The Cartesian Coordinate Planeor Rectangular Coordinate System

  4. Quadrants

  5. Example Plotting Data on U.S. Exports to Mexico The table gives the number of cars produced in the United States between 1997 and 2004. Plot the (year, annual production) ordered pairs in a rectangular coordinate system.

  6. Solution Plotting Data on U.S. Exports to Mexico

  7. Absolute Value of a Real Number

  8. Example Using the Definition of Absolute Value

  9. Solution

  10. Properties of Absolute Value

  11. Distance Formula (Number Line)

  12. Distance Formula (Coordinate Plane)

  13. The Distance Formula using the Pythagorean Theorem

  14. Example Finding the Distance Between Two Points 

  15. Solution 

  16. Midpoint Formula (Number Line)

  17. Midpoint Formula (Coordinate Plane)

  18. Standard Form Equation of a Circle

  19. Standard Form Equation of a Circle

  20. Example Finding Standard Form Equations of Circles

  21. Example Finding Standard Form Equations of Circles

  22. Quick Review

  23. Quick Review Solutions

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