1. 04 Introduction to Analytic Geometry College Algebra

2. 4.1 Coordinate Systems Origin Line Plane Point Coordinate (a,b) same as (x,y) Units Three Space (a,b,c)

3. Dimensions 1-D 2-D 3-D a0b y x y x z

4. Dimensions 1-D 2-D 3-D a0b y x y x z

5. Coordinate System Review y x III III IV Origin

6. Line vs Line Segment y x y = mx + b

7. Line vs Line Segment y x AB A B

8. Ordered Pairs Review : (a,b) b a III III IV (a,b)(-a,b) (a,-b) (-a,-b)

9. Transformations & Coordinate Geometry

10. Transformations – Model Motion Translation – Glide or Slide Rotation – (about an axis) Reflection – Mirror image Dilation – larger or smaller

11. Terminology Image – final image after transformation Labeled with “Prime” Pre-image – image before transformation Labeled with Capital Letters A A’ B B’ Pre-ImageImage Horizontal Translation

12. Translation Pre-ImageImage Slide Arrow A B C A’ B’ C’

13. Rotation – 90  180  270  45  Pre-Image Image 90  Image 180  Image 270  Note: Example Rotation is Clockwise

14. Reflection Mirror Line Pre-Image Image

15. Graphing Motion ( x, y )  ( x + h, y )  ( x, y + v )  ( x, -y )  ( -x, y )  ( -x, -y )  ( nx, ny ) Pre-ImageImage Horizontal Translation Vertical Translation Reflection through x-axis Reflection through y-axis 180 Rotation about Origin Dilation

16. Back to the text… Distance Formula 1-D 2-D 3-D

17. 1-D | b-a | or | a-b | a0b

18. 2-D: “THE” Distance formula what do you know about the distance formula???

19. 2-D: “THE” Distance formula A B

20. A B

21. (-3,2) (5,7) d = sqrt((5- -3) 2 + (7-2) 2 )

22. 2-D: “THE” Distance formula (-3,2) (5,7) d = (5- -3) 2 + (7-2) 2

23. 2-D: “THE” Distance formula (-3,2) (5,7) d = (8) 2 + (5) 2

24. 2-D: “THE” Distance formula (-3,2) (5,7) d = 64 + 25

25. 2-D: “THE” Distance formula (-3,2) (5,7) d = 89 = 9.434

26. Who can do the Pythagorean Theorem? (-3,2) (5,7) d ( 5,2)

27. Who can do the Pythagorean Theorem? (-3,2) (5,7) d = 8 2 + 5 2 ( 5,2) d 8 5

28. Who can do the Pythagorean Theorem? (-3,2) (5,7) d = 64 + 25 ( 5,2) d 8 5

29. The distance formula and the Pythagorean Theorem are very similar.