NAME GEOMETRY NOTES UNIT 6 COORDINATE GEOMETRY

NAMEGEOMETRY NOTESUNIT 6COORDINATE 98,9TOPICSolve equations for y mx bWrite equations given slope and y –intercept.Graph linear equationsFind slope given two pointsWrite equation of a line given two pointsand y-interceptEquations of lines parallel andperpendicular to each otherWrite the equations of lines parallel andperpendicular through a given point.More EquationsQUIZFind Midpoint and Distance1/101/1310xxFind Perpendicular BisectorPractice perpendicular bisector1/14111/151/1612/1314QUIZProving things about linesProving Types of triangles/TrapezoidProving 8QUIZProving RectanglesProving RhombusProving SquaresREVIEW FOR MIDTERMSREVIEW FOR MIDTERMSProve a figure is .ReviewTEST1HOMEWORKPg 169# 1, 4, 5, 6, 33, 34.*Graph Paper*Parallel Lines in the CoordinatePlane Worksheet #1, 3, 4, 6, 7, 8, 9,13, 15, 17Pg 177# 1, 2, 6, 8, 10, 16, 18, 26Pg 178# 12, 14, 20, 22No HOMEWORK!Distance/Midpoint Worksheet.Circled QuestionsNO HOMEWORK!Finish In Class Assignment if notdone.Pg 351 #12-16Pg 353 #42-44Worksheet HW tri/trapsWorksheet Prove JOHN is aparallelogramWorksheet Prove WARD is arectangleWorksheet Prove DROW is arhombusWorksheet Prove ANDY is a squareTBDSTUDYNo HomeworkTICKET-INNo Homework

Solve for y/Write equation of a line/GraphThe general equation for a line is wherem b ------2

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---Hmmm.looks like the lines areSo always havethe slope!---Hmmm.looks like the lines areSo always havethe slope!4

Remember:Lines that are parallel haveLines that are perpendicular have----5-

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Midpoint of a line segmentMidpoint Formula: The midpoint M of AB with endpoints A(x1,y1) and B(x2,y2) are the following:--Hmm looks like thelineseach other!- -8

----Note: When finding the distance between two pointsyou can either use the Pythagorean Theorem or the distance formula.9

PERPENDICULAR BISECTORRemember:Equation of a line: where m and b Perpendicular lines have:To bisect a line you find theIf the endpoints of a line segment are given as (-3,5) and (7,7), find the perpendicular bisector of the linesegment:Follow these steps:1.) Find the slope of the line segment:2.) Write the slope of a line that would be perpendicular to that line:3.) What is the midpoint of the segment?4.) What is the y-intercept of a line with the slope from #2 andthat goes through the point from #3?5.) What is the equation of a line with the slope from #2 and the y-intercept from #4?Now you try:6.) Find the perpendicular bisector of the segment joining thepoints (-10,-4) and (-2,0)10

PROVING THINGS ABOUT LINESWHAT TO PROVEHOW TO PROVEFORMULA TO USELines are PARALLELLines are NOT PARALLELLines are PERPENDICULARLines BISECT EACH OTHERLines are CONGRUENT1.) Prove that AB and CD bisect each other ifA(-1,-3) B(3,3)C(-3,3) D(5,-3)2.) Prove EF GH ifE(2,-2) F(4,2)G(1,1) H(5,-1)3.) Prove that WX YZ ifW(1,1) X(5,4) Y(-2,-5) Z(2,-2)4.) Prove that MN PO ifM(-8,1) N(-2,-1) O(3,2) P(1,-4)11

PROVING TRIANGLES/TRAPEZOIDS1.) Given: R(1,-1), U(6,-1), N(1,-7).Prove: RUN is a right triangle2.)What are we really trying to do?How are we going to do that?Come up with a plan. What are youtrying to do? How are you going to do it?WRITE IT!!!Given: R(-4,0), I(0,1), C(4,-1), K(-4,1)12

3.)---- -- -13

PROVING PARALLELOGRAMS USING COORDINATE GEOMETRY-2.) If three of the points of a parallelogram are (-1,2), (4,6), (6,0) find the other point. Justify your answer:14

PROVING RECTANGLES USING COORDINATE GEOMETRYWAYS TO PROVEHOW ARE WE GOING TO DO THIS USINGCOORDINATE GEOMETRY?1.) Prove that it is a PARALLELOGRAM with2.) Prove that it is a PARALLELOGRM with3.) Prove that all angles areLet’s pick a way and stick with it!--2.) Find the coordinates of E if CHER is a Rectangle C(0,2) H(4,8) E(x,y) R(3,0). Justify your answer.15

PROVING RHOMBUSES USING COORDINATE GEOMETRYWAYS TO PROVEHOW ARE WE GOING TO DO THIS USINGCOORDINATE GEOMETRY?1.) Prove that it is a PARALLELOGRAM with2.) Prove that it is a PARALLELOGRAM with3.) Prove that all sides areLet’s pick a way and stick with it!!!!!--2.) If the coordinates of RHOM are R(-1,5), H(-4,1), O(-1,-3), M(x,y) . Find x &y. Justify your answer.16

PROVING A SQUARE USING COORDINATE GEOMTERYWAYS TO PROVEHOW ARE WE GOING TO DO THIS USINGCOORDINATE GEOMETRY?1.) Prove that it is a RECTANGLE with2.) Prove that it is a RHOMBUS with--- -2.) If SQUA is a square, find the coordinates of S(a,b) given Q(-4,-4), U(2,2), A(8,-4). Justify your answer.17

WHAT SHAPE?1.)If quadrilateral ABCD has coordinates:ABCD? Justify your answer., what type of quadrilateral is2.) If quadrilateral ABCD has coordinates:ABCD? Justify your answer., what type of quadrilateral is18

PROVING RECTANGLES USING COORDINATE GEOMETRY WAYS TO PROVE HOW ARE WE GOING TO DO THIS USING COORDINATE GEOMETRY? 1.) Prove that it is a PARALLELOGRAM with 2.) Prove that it is a PARALLELOGRM with 3.) Prove that all angles are Let’s pick a way and stick with it! - - 2.) Find the coordinates