The Coordinate Plane Table of Contents Introduction Vocabulary - PDF document

Slide 1 / 52 Slide 2 / 52 The Coordinate Plane Table of Contents Introduction Vocabulary Graphing ordered pairs Function Families Slide 3 / 52 Slide 4 / 52 The development of the Coordinate or Cartesian plane is often credited to the French philosopher and mathematician, Rene Descartes. It is said that Descartes first came up with the idea for the plane as he lay in bed watching several flies crawl across his tiled ceiling; as he observed their movement he realized that he could use the intersecting lines formed by the tiles to describe a fly’s location. Although historical evidence suggests that a contemporary of Descartes, Pierre de Fermat, did more to develop " Introduction the coordinate system, Rene Descartes’ work certainly revolutionized mathematics by describing the properties of the plane and using it as the first systematic link between Euclidean geometry and algebra. " Cogito,ergo sum Pierre, bring me my fly swatter! (1,1) x (-1,-1) Rene Descartes (2,-2) 1596 - 1650 y The well known quote; "Cogito,ergo sum" Fun Fact (I think,therefore I am) is Return to attributed to Rene Descartes. Table of Contents Return to table of contents Slide 5 / 52 Slide 6 / 52 0 VOCABULARY The coordinate plane is divided into four sections called quadrants. Each quadrant is numbered using the Roman numerals I through IV, in a counter-clock wise direction. Return to Table of Contents

Slide 7 / 52 Slide 8 / 52 c Slide the "C" onto the y - axis 0 coordinate plane x - axis 0 The Coordinate plane is also called the Cartesian plane. The quadrants are formed by two intersecting number lines called axes. One way to remember how the quadrants are numbered is to The horizontal line is the x-axis. The vertical line is the y-axis. write a big "C" on top of the plane. The "C" will begin in quadrant I and end in quadrant IV. Slide 9 / 52 Slide 10 / 52 Origin (0, 0) 0 0 The point at which the x and y axes intersect is called the origin. Points can be plotted on the plane using one coordinate from each The coordinates of the origin are (0, 0). of the axes. These sets are called ordered pairs. The x coordinate always appears first in these pairs. The y coordinate appears second. (x, y) Slide 11 / 52 Slide 12 / 52 Each of the quadrants can be identified by the properties of the 1 What points are in quadrant II ? numbers that fall within their plane. Remember the ordered pairs are always of the form (x, y) A B A C F D (-,+) ( +,+) D E E 0 F G G B H C (+,-) (-,-)

Slide 13 / 52 Slide 14 / 52 2 What points are in quadrant I ? 3 What points are in quadrant IV ? A A B B A A C C F F D D D D E E E E F F G G G G B B H H C C Slide 15 / 52 Slide 16 / 52 5 What point is closest to the origin? 4 What points are in quadrant III ? A A is B B A C F A C F D D E E D D E F G E G B F H C G G B H C Return to table of contents Slide 17 / 52 Slide 18 / 52 To 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 second Graphing Ordered Pairs number · plot the point (3,2) Return to Table of Contents

Slide 19 / 52 Slide 20 / 52 To graph (-3, 4): To graph (-3, -2): Start at the origin and then move Start at the origin and then move 3 left, up 4 3 left, down 2 (-3, 4) (-3, -2) Slide 21 / 52 Slide 22 / 52 To graph (5, -3): Place the star on (2,8) in Start at the origin and then move quadrant I 5 right, down 3 Place the triangle on (-4, 4) in quadrant II Place the square on (-7, -3) in quadrant III Place the circle on (1, -4) in quadrant IV (5, -3) Slide 23 / 52 Slide 24 / 52 Match the coordinate points below with points A-F on the coordinate plane. Move each rainbow circle to check your Place the circle on (-7,-5) answers. Place the star on (4,9) (-9,-4) D Place the triangle on (-6,2) A F (2,-2) E Place the square on (9,0) B C (3,-9) B (0,6) F In which quadrant is the circle? E (5,7) A D C (-3,2)

Slide 25 / 52 Slide 26 / 52 6 The point (-5, 4) is located in quadrant_____. 7 The point (7, -2) is located in quadrant _____. A I A I B II B II C III C III D IV D IV Slide 27 / 52 Slide 28 / 52 8 The point (4, 5) is located in quadrant ____. 9 The quadrant where the x & y coordinates are both negative is quadrant ___. A I A I B II B II C III C III D IV D IV Slide 29 / 52 Slide 30 / 52 10 When plotting points in the Cartesian Plane, you always List the coordinates of each start at ____. point E A A A the x - axis B B the origin F C D C the y-axis D D the Coordinate Plane C E B E (0,0) F

Slide 31 / 52 Slide 32 / 52 C List the coordinates of each List the coordinates of each point point A E B F A A B B D E C C D A D D C B E E F F F Slide 33 / 52 Slide 34 / 52 Open ended Questions Remember to: *Read the question carefully and think about the answer. *Answer all parts of the question. *Show your work and explain your answer. You can answer the questions using words, tables, diagrams or pictures. Slide 35 / 52 Slide 36 / 52 Vocabulary Review 11 If the x-coordinate is positive, the point to be plotted will Coordinate Plane: the two dimensional plane or flat surface that be in quadrant _____. is created when the x-axis intersects with the y-axis. Also known as a coordinate graph and the Cartesian plane. Quadrant: any of the four regions A I created when the x-axis intersects the y-axis. They are usually numbered with Roman II I B I & II numerals. C I & IV x-axis: horizontal number line that extends indefinitely in IV D II III both directions from zero. (Right- positive Left- negative) y-axis: vertical number line that extends indefinitely in both directions from zero. (Up- positive Down- negative) Origin: the point where zero on the x-axis intersects zero on the y-axis. The coordinates of the origin are (0,0).

Slide 37 / 52 Slide 38 / 52 12 If the y-coordinate is positive, the point to be plotted will 13 If the x - coordinate is negative and the y-coordinate is be in quadrant _____. positive, the point to be plotted will be in quadrant _____. A A I I B I & II B I & II C I & IV C I & IV D II D II Slide 39 / 52 Slide 40 / 52 14 If the x - coordinate is positive and the y-coordinate is 15 Point A is located at (-3, 2) negative, the point to be plotted will be in quadrant _____. True A I False B II C III D IV A Slide 41 / 52 Slide 42 / 52 16 Point A is located at (-5, 1) 17 Point A is located at (-2, 3) True True A False False A

Slide 43 / 52 Slide 44 / 52 18 Point A is located at (-2, 0) Function Families True False A family of functions is a group of functions with shared traits. The parent function is the most basic function in a family. A Return to Table of Contents Slide 45 / 52 Slide 46 / 52 Absolute Value Functions Linear Functions Fill in the table for y = l x l The parent function for all linear functions is y = x Then plot the points and connect them. Complete the table, plot the points and then connect them. X Y y = x -4 X Y -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 Put arrows at the end of the line to indicate the line goes on forever. PULL PULL Slide 47 / 52 Slide 48 / 52 Quadratic Functions Match the correct equation with the graphed function Complete the table for y = x 2 Then plot the points and connect them y = x y = x 2 y = l x l X Y -3 -2 -1 0 1 2 3 PULL PULL

Slide 49 / 52 Slide 50 / 52 The function graphed is y = x 2 19 The function graphed is y = x 20 Yes Yes No No Slide 51 / 52 Slide 52 / 52 21 The function graphed is y = l x l Yes No