The Coordinate Plane - NJCTL
The Coordinate PlaneSlide 1 / 52Slide 2 / 52Table of ContentsIntroductionVocabularyGraphing ordered pairsFunction FamiliesSlide 3 / 52IntroductionReturn toTable of Contents
The development of the Coordinate or Cartesian plane is often credited tothe French philosopher and mathematician, Rene Descartes. It is said thatDescartes first came up with the idea for the plane as he lay in bedwatching several flies crawl across his tiled ceiling; as he observed theirmovement he realized that he could use the intersecting lines formed bythe tiles to describe a fly’s location. Although historical evidence suggeststhat a "contemporary of Descartes, Pierre de Fermat, did more to developthe coordinate system, Rene Descartes’ work certainly revolutionizedmathematics by describing the properties of the plane and using it as thefirst systematic link between Euclidean geometry and algebra.Cogito,ergo sumSlide 4 / 52"Pierre, bring me my fly swatter!(1,1)x(-1,-1)Rene Descartes1596 - 1650(2,-2)yThe well known quote;"Cogito,ergoFun Fact sum"(I think,therefore I am) isattributed to Rene Descartes.Return to table ofcontentsSlide 5 / 52VOCABULARYReturn toTable of ContentsSlide 6 / 520The coordinate plane is divided into four sections called quadrants.Each quadrant is numbered using the Roman numerals I through IV, ina counter-clock wise direction.
Slide the "C"onto thecoordinate planecSlide 7 / 520The Coordinate plane is also called the Cartesian plane.One way to remember how the quadrants are numbered is towrite a big "C" on top of the plane. The "C" will begin inquadrant I and end in quadrant IV.Slide 8 / 52y - axis0x - axisThe quadrants are formed by two intersecting number lines calledaxes.The horizontal line is the x-axis. The vertical line is the y-axis.Slide 9 / 520Origin(0, 0)The point at which the x and y axes intersect is called the origin.The coordinates of the origin are (0, 0).
Slide 10 / 520Points can be plotted on the plane using one coordinate from eachof the axes.These sets are called ordered pairs. The x coordinate alwaysappears first in these pairs. The y coordinate appears second.(x, y)Each of the quadrants can be identified by the properties of thenumbers that fall within their plane. Remember the ordered pairsare always of the form (x, y)Slide 11 / 52( , )(-, )0( ,-)(-,-)1Slide 12 / 52What points are in quadrant II ?ABACDEDFEFGHGBC
2Slide 13 / 52What points are in quadrant I ?ABACDEDFEFGH3GBCSlide 14 / 52What points are in quadrant IV ?ABACDEDFEFGH4GBCSlide 15 / 52What points are in quadrant III ?ABACDEDFEFGHGBC
5Slide 16 / 52What point is closest to the origin?AisBACDEDFEFGHGBCReturn to table ofcontentsSlide 17 / 52Graphing Ordered PairsReturn toTable of ContentsSlide 18 / 52To graph an ordered pair, such as (3,2):· start at the origin (0,0)· move left or right on the x-axis depending on the first number· then move up or down from there depending on the secondnumber· plot the point(3,2)
To graph (-3, 4):Start at the origin and then move3 left, up 4Slide 19 / 52(-3, 4)Slide 20 / 52To graph (-3, -2):Start at the origin and then move3 left, down 2(-3, -2)Slide 21 / 52To graph (5, -3):Start at the origin and then move5 right, down 3(5, -3)
Slide 22 / 52Place the star on (2,8) inquadrant IPlace the triangle on (-4, 4) inquadrant IIPlace the square on (-7, -3)in quadrant IIIPlace the circle on (1, -4) inquadrant IVSlide 23 / 52Place the circle on (-7,-5)Place the star on (4,9)Place the triangle on(-6,2)Place the square on(3,-9)In which quadrant is thecircle?Match the coordinate points below with points A-F on thecoordinate plane. Move each rainbow circle to check A(-3,2)CSlide 24 / 52
The point (-5, 4) is located in quadrant .6AIBIICIIIDIVThe point (7, -2) is located in quadrant .7AIBIICIIIDIVThe point (4, 5) is located in quadrant .8AIBIICIIIDIVSlide 25 / 52Slide 26 / 52Slide 27 / 52
The quadrant where the x & y coordinates are bothnegative is quadrant .9AIBIICIIIDIVWhen plotting points in the Cartesian Plane, you alwaysstart at .10Athe x - axisBthe originCthe y-axisDthe Coordinate PlaneE(0,0)Slide 28 / 52Slide 29 / 52Slide 30 / 52List the coordinates of eachpointEAABFDCBCDEF
Slide 31 / 52AList the coordinates of eachpointEBABCDDCFEFSlide 32 / 52CList the coordinates of eachpointFABDEABCDEFOpen ended QuestionsRemember to:*Read the question carefully andthink about the answer.*Answer all parts of the question.*Show your work and explain youranswer.You can answer the questions usingwords, tables, diagrams or pictures.Slide 33 / 52
Slide 34 / 52Vocabulary ReviewSlide 35 / 52Coordinate Plane: the two dimensional plane or flat surface thatis created when the x-axis intersects with the y-axis. Also knownas a coordinate graph and the Cartesian plane.IIIIVIIIQuadrant: any of the four regionscreated when the x-axisintersects the y-axis. They areusually numbered with Romannumerals.x-axis: horizontal number linethat extends indefinitely inboth directions from zero.(Right- positive Left- negative)y-axis: vertical number line that extends indefinitely in bothdirections from zero. (Up- positive Down- negative)Origin: the point where zero on the x-axis intersects zero onthe y-axis. The coordinates of the origin are (0,0).If the x-coordinate is positive, the point to be plotted willbe in quadrant .11AIBI & IICI & IVDIISlide 36 / 52
If the y-coordinate is positive, the point to be plotted willbe in quadrant .12AIBI & IICI & IVDIIIf the x - coordinate is negative and the y-coordinate ispositive, the point to be plotted will be in quadrant .13AIBI & IICI & IVDIIIf the x - coordinate is positive and the y-coordinate isnegative, the point to be plotted will be in quadrant.14AIBIICIIIDIVSlide 37 / 52Slide 38 / 52Slide 39 / 52
15Slide 40 / 52Point A is located at (-3, 2)TrueFalseA16Slide 41 / 52Point A is located at (-5, 1)TrueFalseA17Slide 42 / 52Point A is located at (-2, 3)TrueFalseA
Slide 43 / 5218Point A is located at (-2, 0)TrueFalseASlide 44 / 52Function Familie sA family of functions is a group of functions with shared traits.The parent function is the most basic function in a family.Return toTable of ContentsSlide 45 / 52Linear FunctionsThe parent function for all linear functions is y xComplete the table, plot the points and then connect them.y xXY-3-2-10123Put arrows at the end of the line to indicate the line goes on forever.PULL
Slide 46 / 52Absolute Value FunctionsFill in the table for y l x lThen plot the points and connect them.XY-4-3-2-101234PULLSlide 47 / 52Quadratic FunctionsComplete the table for y x2Then plot the points and connect themXY-3-2-10123PULLSlide 48 / 52Match the correct equation with the graphed functiony xy x2y lxlPULL
19 The function graphed is y xSlide 49 / 52YesNo20 The function graphed is y x2Slide 50 / 52YesNo21 The function graphed is y l x lYesNoSlide 51 / 52
Slide 52 / 52
The Coordinate plane is also called the Cartesian plane. One way to remember how the quadrants are numbered is to write a big "C" on top of the plane. The "C" will begin in quadrant I and end in quadrant IV. Slide the "C" onto the coordinate plane Slide 7 / 52 0 The quadrants are formed by two intersecting number lines called axes.
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