Cartesian Plane Polygons in the Coordinate Plane Cartesian Plane - PDF document

Slide 1 / 107 Slide 2 / 107 6th Grade Graphing 2015-12-02 www.njctl.org Slide 3 / 107 Slide 4 / 107 Graphing 6th Grade Topics Click on the topic to go to that section · Cartesian Plane · Graphing Ordered Pairs Cartesian Plane · Polygons in the Coordinate Plane · Cartesian Plane Applications · Glossary & Standards Return to Table of Contents Slide 5 / 107 Slide 6 / 107 Cartesian Plane History Cartesian Plane History Although historical evidence suggests that a contemporary of The development of the Coordinate or Cartesian plane is often Descartes, Pierre de Fermat, did more to develop the coordinate credited to the French philosopher and mathematician, Rene system, Rene Descartes’ work certainly revolutionized Descartes. mathematics by describing the properties of the plane and using it as the first systematic link between Euclidean geometry and It is said that Descartes first came up with the idea for the plane as he algebra. 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. x "Cogito,ergo sum" Rene Descartes 1596 - 1650 y

Slide 7 / 107 Slide 8 / 107 Coordinate Plane Coordinate Plane c 0 Slide the "C" onto the 0 0 coordinate plane 0 The Coordinate plane is also called the Cartesian plane . The coordinate plane is divided into four sections called quadrants . One way to remember how the quadrants are numbered is to Each quadrant is numbered using the Roman numerals I through write a big "C" on top of the plane. The "C" will begin in IV, in a counter-clockwise direction. quadrant I and end in quadrant IV. Slide 9 / 107 Slide 10 / 107 Coordinate Plane Coordinate Plane Axes Origin y - axis (0, 0) 0 0 x - axis 0 The quadrants are formed by two intersecting number The point at which the x and y axes intersect is called the origin . lines called axes. The horizontal line is the x-axis . The coordinates of the origin are (0, 0). The vertical line is the y-axis . Slide 11 / 107 Slide 12 / 107 Coordinate Plane Ordered Pairs Each of the quadrants can be identified by the properties of the numbers that fall within their plane. Remember the ordered pairs are always of the form (x, y) 0 (-,+) ( +,+) 0 Points can be plotted on the plane using one coordinate from each 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 13 / 107 Slide 14 / 107 1 What points are in quadrant II ? 2 What points are in quadrant I ? A A B B A A F F C C D D D D E E E E F F B B C C Slide 15 / 107 Slide 16 / 107 3 What points are in quadrant IV ? 4 What points are in quadrant III ? A A B B A A F F C C D D D D E E E E F F B B C C Slide 17 / 107 Slide 18 / 107 5 What point is closest to the origin? A B A F C D D E Graphing Ordered Pairs E F B C Return to Table of Contents

Slide 19 / 107 Slide 20 / 107 Ordered Pairs Ordered Pairs To graph an ordered pair, such as (3, 2): To graph (-3, 4): · start at the origin (0, 0) Start at the origin and then move · move left or right on the x-axis depending on the first number 3 left, up 4 · then move up or down from there depending on the second number · plot the point (-3 , 4) (3 , 2) Slide 21 / 107 Slide 22 / 107 Ordered Pairs Ordered Pairs 1 To graph (-3 , -2): To graph (5, -3.25): 2 Start at the origin and then move Start at the origin and then move 3 and a half left, down 2 5 right, down 3.25 (-3 , -2) 1 2 (5 , -3.25) Slide 23 / 107 Slide 24 / 107 Ordered Pairs Practice Ordered Pairs Practice Place the circle on (-7, -5) Place the star on (2.5, 8) in quadrant I 1 Place the star on (4 , 9) 3 Place the triangle on (-4, 4) in Place the triangle on quadrant II (-6.25, 2) 1 Place the square on (-7, -3 ) 2 Place the square on in quadrant III (3, -9) Place the circle on (1, -4) in In which quadrant is the quadrant IV circle?

Slide 25 / 107 Slide 26 / 107 Ordered Pairs Practice Ordered Pairs Practice The points (4, 3) and (-4, 3) show a reflection across the y-axis. Place the circle on (-4, -3) What generalization can Place the star on (4, 3) you make about the coordinates of a point when it is reflected Place the triangle on across the y-axis? (-4, 3) Place the square on (4, -3) What do you notice about the location of the points in relation to each other? What patterns do you see in the coordinates of the points? Slide 27 / 107 Slide 28 / 107 Ordered Pairs Practice Ordered Pairs Practice The points (4, 3) and The points (4, 3) and (4, -3) show a reflection (-4, -3) show a reflection across the x-axis. across both the x-axis and y-axis. What generalization can you make about the What generalization can coordinates of a point you make about the when it is reflected coordinates of a point across the x-axis? when it is reflected across the x-axis and y-axis? Slide 29 / 107 Slide 30 / 107 Ordered Pairs Practice 6 The point (-5, 4) is located in quadrant_____. Move the letter to match it to the correct coordinate point. Then move the circle to check your answer. A I A D (-9, -4.5) F B II E (2, -2) III C C B D IV 1 (9 , 0) B 4 E D (0, 6) F 1 A (5.25, 7 ) 3 C (-3, 2)

Slide 31 / 107 Slide 32 / 107 7 The point (7, -2) is located in quadrant _____. 8 The point (4, 5.75) is located in quadrant ____. A I A I B II B II C III C III D IV IV D Slide 33 / 107 Slide 34 / 107 9 The quadrant where the x & y coordinates are both 10 When plotting points in the Cartesian Plane, you negative is quadrant ___. always start at ____. A the x-axis I A B the origin B II C the y-axis C III D IV the Coordinate Plane D E (0,0) Slide 35 / 107 Slide 36 / 107 11 Point A is plotted on the coordinate plane. 12 Point A is plotted on the coordinate plane. Point A is reflected Point A is reflected across the y-axis. across the x-axis. What are the What are the A A coordinates of the coordinates of the reflection of point reflection of point A? A? A (4, 6) A (4, 6) B (-4, 6) B (-4, 6) C (4, -6) C (4, -6) D (-4, -6) D (-4, -6)

Slide 37 / 107 Slide 38 / 107 13 Point B is plotted on the coordinate plane. 14 Point B is plotted on the coordinate plane. Point B is reflected Point B is reflected across the x-axis. across the y-axis. What are the What are the coordinates of the coordinates of the reflection of point reflection of point B B B? B? A (5, 2) A (5, 2) B (-5, 2) B (-5, 2) C (5, -2) C (5, -2) D (-5, -2) D (-5, -2) Slide 39 / 107 Slide 40 / 107 15 Point C is plotted on the coordinate plane. 16 Point D is plotted on the coordinate plane. Point C is reflected Point D is reflected across the x-axis across the x-axis and y-axis. After and y-axis. After both reflections, both reflections, what are the what are the coordinates of point coordinates of point C? D? A (3, 5) A (2, 9) B (-3, 5) B (-2, 9) D C (3, -5) C (2, -9) C D (-3, -5) D (-2, -9) Slide 41 / 107 Slide 42 / 107 Ordered Pairs Practice 17 Point Q is plotted on the coordinate plane. Students type their answers here List the coordinates of each point E A A B F C D Point Q is reflected across the x-axis. D C What are the coordinates of the reflection of point Q? B E (___,___) F From PARCC EOY sample test non-calculator #11

Slide 43 / 107 Slide 44 / 107 Ordered Pairs Practice Ordered Pairs Practice List the coordinates of each C List the coordinates of each point point A E B A F A B B C D E C D D A D C B E E F F F Slide 45 / 107 Slide 46 / 107 19 If the y-coordinate is positive, the point to be plotted 18 If the x-coordinate is positive, the point to be plotted will be in quadrant _____. will be in quadrant _____. A I A I B I & II I & II B I & IV C C I & IV II D D II Slide 47 / 107 Slide 48 / 107 20 If the x - coordinate is negative and the y- coordinate 21 If the x - coordinate is positive and the y- coordinate is is positive, the point to be plotted will be in quadrant negative, the point to be plotted will be in quadrant _____. _____. A I A I B II B I & II C III I & IV C D IV D II

Slide 49 / 107 Slide 50 / 107 22 Point A is located at (-3, 2) 23 Point A is located at (-5, 1) True True False False A Slide 51 / 107 Slide 52 / 107 24 Point A is located at (-2.5, 3) True False A Polygons in the Coordinate Plane Return to Table of Contents Slide 53 / 107 Slide 54 / 107 Polygons Polygons We can use coordinates as vertices , and connect the dots to draw polygons on a coordinate plane. Point A and point B have been plotted. B C A (2, 1) B B (2, 4) D A List 4 possible A coordinates for point C that would form a right triangle. Plot point C to check. C