Rational Numbers And The Coordinate Plane Math 6

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Rational NumbersRational numbers are numbers that can be written in the form of:𝒑𝒒where 𝑝 and 𝑞 are integers and 𝑞 is not zeroSimilar to integers, rational numbers can be plotted or graphed on thecoordinate plane. What is a coordinate plane?The Coordinate PlaneThe coordinate plane is composed of two number lines, one of which isvertical and the other one is horizontal.2-3-2-1012130Horizontal number line-1-2-3Copyright MathTeacherCoach.com1Vertical number line3

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6These number lines make a perpendicular intersection and meet at acommon point called the origin, with coordinates (0. 0). The horizontalnumber line is called the x-axis and the vertical number line is calledthe y-axis.yorigin(0, 0)y axisxyx axisCopyright MathTeacherCoach.com2

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Sample Problem 1: Label the parts of the coordinate plane and fill outany missing values.yoriginy axisxyx axisCopyright MathTeacherCoach.com3

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6The QuadrantsWhen the horizontal number line(x-axis) and the vertical numberline (y-axis) meet at the originwith point (0, 0), four regionscalled quadrants are formed.These quadrants are labeled withRoman numerals I – IV in acounterclockwise manner.yxPoints in the Coordinate PlaneThe coordinate plane is made up ofinfinitely many points. Take a lookat point A.yAy(x, y)xxCopyright MathTeacherCoach.com4Drawing a line perpendicular fromthe given point to the x axis andanother line perpendicular to the yaxis determines the location of thepoint in the coordinate plane.

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided Notesy(x, y)xMath 6To avoid confusion, we locate pointA by giving the number x first,then the number y. This will formthe ordered pair or coordinates(x, y). This pair of numberscorresponds to point A.The first number x is called the xcoordinate or the abscissa, whilethe second number y is the secondcoordinate or the ordinate.(x, y)(first coordinate, second coordinate)(x coordinate, y coordinate)(abscissa, ordinate)Copyright MathTeacherCoach.com5

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Sample Problem 2: Complete the table by giving the x coordinate and ycoordinate of the given points.Points in the Coordinate Planex coordinatey coordinate1. A-192. B1183. C54. D205. E-666. F-9-107. G008. H-250Copyright MathTeacherCoach.com6

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Describing the Points in each QuadrantThe coordinates in each quadrant of the coordinate plane varies. Take alook at the illustration below:y( -x, y)( x, y)x( x, - y)( -x, - y)In Quadrant I:The x coordinate and the y coordinate are both positive.In Quadrant II:The x coordinate is negative and the y coordinate is positive.In Quadrant III:The x coordinate and the y coordinate are both negative.In Quadrant IV:The x coordinate is positive and the y coordinate is negative.Copyright MathTeacherCoach.com7

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Describing the Points on the Axesyy axis( 0, y)x axis( x, 0)xx axis( -x, 0)y axis( 0, -y)In the x axis:The x coordinate to the right of 0 is positive and the y coordinate is 0.The x coordinate to the left of 0 is negative and the y coordinate is 0.In the y axis:The y coordinate above 0 is positive and the x coordinate is 0.The y coordinate below 0 is negative and the x coordinate is 0Copyright MathTeacherCoach.com8

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Example: Tell where the following points are located in the coordinateplane.y1.2.3.4.5.6.𝑨Point M is located inQuadrant I because boththe x and y coordinatesare positive.𝟏𝟓𝑴 𝟒𝟕𝑷 𝟒𝟎Point A is located inQuadrant II because thex coordinate is negativeand the y coordinate ispositive.𝑻𝟔x𝟐𝑸 𝟎𝟕𝑯 𝟓𝟕Point T is located in Quadrant III because the x coordinate and they coordinate are both negative.Point H is located in Quadrant IV because the x coordinate isnegative and the y coordinate is positive.Point P is on the x axis because the y coordinate is 0.Point Q is on the y axis because the x coordinate is 0.Copyright MathTeacherCoach.com9

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Sample Problem 3: Determine the location of the given points on thecoordinate t II6.Solution:Quadrant III2.Solution:Quadrant III7.Solution:Quadrant IV3.Solution:y axis8.Solution:x axis4.Solution:Origin9.Solution:Quadrant I5.Solution:Quadrant IV10.Solution:Quadrant IICopyright MathTeacherCoach.com10

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Naming Points on the Coordinate PlaneWe follow specific rules in naming points in the coordinate plane.Remember that each point on the coordinate plane is determined by tworational numbers of the form (x, y), where x is the first coordinate and yis the second coordinate. So, we’ll name it using the numbers on the x axisfirst, followed by the number on the y axis. Take a look at the points onthe coordinate plane. What are the coordinates of the given points?Let’s start with point A.AThe x-coordinate of point Adescribes the point’s positionin relation to the x-axis.Drawing a line from the pointto the x-axis, the x-coordinateof point A is 4.tsThe y-coordinate of point Adescribes the point’s positionin relation to the y-axis.Drawing a line from the pointto the y-axis, the y-coordinateof point A is 7.Since the point A is in Quadrant I, the coordinates of point A are bothpositive: ( 4, 7 ).Copyright MathTeacherCoach.com11

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Now, name the coordinatesof point B.A (4, 7)The x-coordinate of point Bdescribesthepoint’sposition in relation to the xaxis. Drawing a line fromthe point to the x-axis, thex-coordinate of point B is 7.B(7, 4)C(-5, 0)The x-coordinate of point Bdescribesthepoint’sposition in relation to the yaxis. Drawing a line fromthe point to the x-axis, thex-coordinate of point B is 4.Since the point B is in Quadrant I, the coordinates of point B are bothpositive: ( 7, 4 ).Name the coordinates of point C.Here point C is 5 units from the y-axis and since point C is on the x-axisto the left of 0, the x-coordinate is -5.It follows that the distance of point C from the x-axis is 0 units;therefore the y-coordinate is 0.Thus, the coordinates of point C is: ( -5, 0 ).Copyright MathTeacherCoach.com12

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Sample Problem 4: Name the following points in the coordinate plane.1. A (-6, 5 )6.F ( -7, 0 )2. B ( 0, 0 )7.G ( -4, -2 )3. C ( 0, 7 )8.H ( 7, -3 )4. D ( 3. -4 )9.I ( 0, -6)5. E ( 4, 2 )10. J ( 2, 4 )yCAJEEFBxGHDICopyright MathTeacherCoach.com13

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Plotting of Points on the Coordinate PlaneIf points on the coordinate plane can be named, points can also be plottedor located in the plane using number pairs also called as their coordinates( x, y ).To locate a point in the coordinate plane, take note of the steps in eachexample.1. Plot point A with coordinates ( 3, 4 ).Since the x coordinate and they coordinate are both positive,point A must be located inQuadrant I.yxFirst, position your pen orpencil at the origin withcoordinates (0, 0).Copyright MathTeacherCoach.com14

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6yFrom that point, move 3 unitsto the right of zero, sincexthe x-coordinate is positive3.yA (3, 4)And from that point, move 4unitsup,sincethey-coordinate is positive 4.xYay! The point right there iswherepointAwithcoordinates (3, 4) must be.Copyright MathTeacherCoach.com15

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 62. Plot point B with coordinates ( 4, 3 ).ySince the x-coordinate andthe y-coordinate are bothB (4, 3)positive, point B must belocated in Quadrant I.xFirst, position your pen orpencil at the origin withcoordinates (0, 0).From that point, move 4units to the right of zero,since the x-coordinate ispositive 4.And from that point, move 3 units up, since the y-coordinate is positive 3.The point right there is where point B with coordinates (4, 3) must be.Copyright MathTeacherCoach.com16

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 63. Plot point C with coordinates ( -5, 2 ).ySince the x-coordinate isnegative and the y-coordinateis positive, point C must belocated in Quadrant II.𝟏C (-5, 2 )𝟐xFrom the origin, move 5 units tothe left of zero, since the xcoordinate is negative 5.And from that point, move 2𝟏D (2 , -5)𝟐units up, since the y-coordinateis positive 2 .4. On the same coordinate plane; plot point D with coordinates (2 , -5 ).Since the x-coordinate is positive and the y-coordinate is negative,point D must be located in Quadrant IV.From the origin, move 2units to the right of zero, since the x-coordinate is positive 2 .And from that point, move 5 units down, since the y-coordinate isnegative 5.Copyright MathTeacherCoach.com17

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided Notes5. Plot point E with coordinates ( 7,).F (0, 7)Since the x-coordinate ispositive and the y-coordinate is0, point E must be located inthe x axis.Math 6yE (7, 0)xFrom the origin, move 7 units tothe right of zero, since the xcoordinate is positive 7.The point stays in that positionsince the y-coordinate is 0.6. On the same coordinate plane; plot point F with coordinates (0, 7).Since the x-coordinate is 0 and the y-coordinate is positive, point Fmust be located in the y-axis.From the origin, there should be no right or left movement since the xcoordinate is 0. Just continue moving 7 units up since the y-coordinate ispositive 7.Copyright MathTeacherCoach.com18

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Now using the examples above, compare the location of the points on thecoordinate plane. What have you observed?A(3, 4)B(4, 3)C(-5, 2 )The order of numbersinthecoordinatespointonA(3, 4)thecoordinate plane.F(0, 7)yaffects the location oftheE(7,0)D(2 , -5)𝟏C(-5, 2 )B(4, 3)𝟐Points A(3, 4) and B(4,3) may have the samenumbersparenthesisinxthebut willE(-7, 0)have different positionson the plane.𝟏D(2 , -5)𝟐The same thing goes forpoints C( -5, 2) andF(0,-7)D(2 , -5 ),and E(7,0)and F(0, 7).Copyright MathTeacherCoach.com19

Name: Period: Date:Rational Numbers and the Coordinate Plane Guided NotesMath 6Sample Problem 5: Plot the following points on the coordinate plane.1.A(0, 0)4. D(6 , 3)7. G(-5, -3)2.B(-2, 4)5. E(4, 0)8. H(5, 3)3.C(4, -2)6. F(0, -4)9. I(5, -3)yB(-2, 4)D(6 , 3)H(5, 3)A(0, 0)E(4, 0)C(4, -2)G(-5, -3)Copyright MathTeacherCoach.comF(0,-4)20I(5, -3)x

Jul 03, 2020 · Plotting of Points on the Coordinate Plane If points on the coordinate plane can be named, points can also be plotted or located in the plane using number pairs also called as their coordinates ( x, y ). To locate a point in the coordinate plane, take note of the steps in