04 Introduction to Analytic Geometry College 4 1 Coordinate Systems Origin Line Plane Point Coordinate a b same as x y Units Three Space a b c Dimensions 1 D 2 D z a y 0 xb y 3 D x Dimensions a 1 D 2 D b y z x 3 D y x 0 Coordinate System Review y II I x Origin III IV Line vs Line Segment y y mx b x Line vs Line Segment y AB B x A Ordered Pairs Review a b a b b II I a b a a b III IV a b Transformations Coordinate Geometry Transformations Model Motion Translation Glide or Slide Rotation about an axis Reflection Mirror image Dilation larger or smaller Terminology Image final image after transformation Labeled with Prime Pre image image before transformation Labeled with Capital Letters B Horizontal Translation A Pre Image B A Image Translation A Pre Image Image B C A B Slide Arrow C Rotation 90 180 270 45 Pre Image Image 270 Image 90 Image 180 Note Example Rotation is Clockwise Reflection Pre Image Im ag e Mirror Line Graphing Motion Pre Image Horizontal Translation Vertical Translation Reflection through x axis Reflection through y axis 180 Rotation about Origin Dilation x x x x x x y y y y y y Image x h y x y v x y x y x y nx ny Back to the text Distance Formula 1 D 2 D 3 D 1 D b a a b a or 0 b 2 D THE Distance formula what do you know about the distance formula 2 D THE Distance formula B A 2 D THE Distance formula B A 2 D THE Distance formula 5 7 3 2 d sqrt 5 3 2 7 2 2 2 D THE Distance formula 5 7 3 2 d 5 3 2 7 2 2 2 D THE Distance formula 5 7 3 2 d 8 2 5 2 2 D THE Distance formula 5 7 3 2 d 64 25 2 D THE Distance formula 5 7 3 2 d 89 9 434 Who can do the Pythagorean Theorem 5 7 d 3 2 5 2 Who can do the Pythagorean Theorem 5 7 d 3 2 d 8 5 5 2 8 2 52 Who can do the Pythagorean Theorem 5 7 d 3 2 d 8 5 5 2 64 25 The distance formula and the Pythagorean Theorem are very similar
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