04 Introduction to Analytic Geometry4.1 Coordinate SystemsDimensionsSlide 4Coordinate System ReviewLine vs Line SegmentSlide 7Ordered Pairs Review : (a,b)Transformations & Coordinate GeometryTransformations – Model MotionTerminologyTranslationRotation – 90° 180° 270° 45° ? °ReflectionGraphing MotionBack to the text…1-D2-D: “THE” Distance formulaSlide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Who can do the Pythagorean Theorem?Slide 27Slide 28The distance formula and the Pythagorean Theorem are very similar.04 Introduction to Analytic GeometryCollege Algebra4.1 Coordinate SystemsOriginLinePlanePointCoordinate (a,b) same as (x,y)UnitsThree Space (a,b,c)Dimensions1-D2-D3-Da 0 byxyxzDimensions1-D2-D3-Da 0 byxyxzCoordinate System ReviewyxIIIIIIIVOriginLine vs Line Segmentyxy = mx + bLine vs Line SegmentyxABABOrdered Pairs Review : (a,b)baIIIIIIIV(a,b)(-a,b)(a,-b)(-a,-b)Transformations & Coordinate GeometryTransformations – Model MotionTranslation – Glide or SlideRotation – (about an axis)Reflection – Mirror imageDilation – larger or smallerTerminologyImage – final image after transformationLabeled with “Prime”Pre-image – image before transformationLabeled with Capital Letters AA’BB’Pre-Image ImageHorizontal TranslationTranslationPre-ImageImageSlide ArrowABCA’B’C’Rotation – 90 180 270 45 Pre-ImageImage90Image180Image270Note: Example Rotation is ClockwiseReflectionMirror LinePre-ImageImageGraphing Motion( x , y )( x , y )( x , y )( x , y )( x , y )( x , y ) ( x + h, y ) ( x , y + v ) ( x , -y ) ( -x , y ) ( -x , -y ) ( nx, ny )Pre-Image ImageHorizontal TranslationVertical TranslationReflection through x-axisReflection through y-axis180 Rotation about OriginDilationBack to the text…Distance Formula1-D2-D3-D1-D | b-a | or | a-b |a 0 b2-D: “THE” Distance formula what do you know about the distance formula2-D: “THE” Distance formulaAB2-D: “THE” Distance formulaAB2-D: “THE” Distance formula(-3,2)(5,7)d = sqrt((5- -3)2 + (7-2)2)2-D: “THE” Distance formula(-3,2)(5,7)d = (5- -3)2 + (7-2)22-D: “THE” Distance formula(-3,2)(5,7)d = (8)2 + (5)22-D: “THE” Distance formula(-3,2)(5,7)d = 64 + 252-D: “THE” Distance formula(-3,2)(5,7)d = 89 = 9.434Who can do the Pythagorean Theorem(-3,2)(5,7)d( 5,2)Who can do the Pythagorean Theorem(-3,2)(5,7)d = 82 + 52( 5,2)d85Who can do the Pythagorean Theorem(-3,2)(5,7)d = 64 + 25( 5,2)d85The distance formula and the Pythagorean Theorem are very