The Coordinate Plane Table of Contents Introduction Vocabulary - - PDF document

the coordinate plane
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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


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The Coordinate Plane

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Introduction Vocabulary Graphing ordered pairs Function Families

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Introduction

Return to Table of Contents

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x (-1,-1) y (1,1) (2,-2)

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 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.

" Pierre, bring me my fly swatter! The well known quote;

"Cogito,ergo sum"

(I think,therefore I am) is attributed to Rene Descartes. Cogito,ergo sum

"

Rene Descartes 1596 - 1650

Fun Fact

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VOCABULARY

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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.

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c

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"

  • nto the

coordinate plane

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The quadrants are formed by two intersecting number lines called axes. The horizontal line is the x-axis. The vertical line is the y-axis. x - axis y - axis

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The point at which the x and y axes intersect is called the origin. The coordinates of the origin are (0, 0).

Origin (0, 0)

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Points can be plotted on the plane using one coordinate from each

  • f the axes.

These sets are called ordered pairs. The x coordinate always appears first in these pairs. The y coordinate appears second.

(x, y)

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( +,+) (-,+)

(-,-) (+,-)

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)

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1 What points are in quadrant II ? A B C D E F G H B A C D E F G

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2 What points are in quadrant I ? A B C D E F G H B A C D E F G

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3 What points are in quadrant IV ? A B C D E F G H B A C D E F G

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4 What points are in quadrant III ? A B C D E F G H B A C D E F G

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5 What point is closest to the origin? A B C D E F G H B A C D E F G

is

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Graphing Ordered Pairs

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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 number · plot the point (3,2)

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To graph (-3, 4): Start at the origin and then move 3 left, up 4 (-3, 4)

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To graph (-3, -2): Start at the origin and then move 3 left, down 2 (-3, -2)

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To graph (5, -3): Start at the origin and then move 5 right, down 3 (5, -3)

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Place the star on (2,8) in quadrant I 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

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Place 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 the circle?

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Match the coordinate points below with points A-F on the coordinate plane. Move each rainbow circle to check your answers.

A F E D B C

(2,-2) (9,0) (0,6) (5,7) (-3,2) A E

B D C

F (-9,-4)

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The point (-5, 4) is located in quadrant_____. A I B II C III D IV

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The point (7, -2) is located in quadrant _____. A I B II C III D IV

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The point (4, 5) is located in quadrant ____. A I B II C III D IV

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The quadrant where the x & y coordinates are both negative is quadrant ___. A I B II C III D IV

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When plotting points in the Cartesian Plane, you always start at ____. A the x - axis B the origin C the y-axis D the Coordinate Plane E (0,0)

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F A B C D E List the coordinates of each point A B C D E F

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SLIDE 6

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List the coordinates of each point A B C D E F A B C D E F

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List the coordinates of each point A B C D E F A B C D E F

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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.

Open ended Questions Slide 34 / 52 Slide 35 / 52

y-axis: vertical number line that extends indefinitely in both directions from zero. (Up- positive Down- negative) x-axis: horizontal number line that extends indefinitely in both directions from zero. (Right- positive Left- negative) Origin: the point where zero on the x-axis intersects zero on the y-axis. The coordinates of the origin are (0,0).

II I III IV

Vocabulary Review

Coordinate Plane: the two dimensional plane or flat surface that 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 created when the x-axis intersects the y-axis. They are usually numbered with Roman numerals.

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If the x-coordinate is positive, the point to be plotted will be in quadrant _____. A I B I & II C I & IV D II

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If the y-coordinate is positive, the point to be plotted will be in quadrant _____. A I B I & II C I & IV D II

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If the x - coordinate is negative and the y-coordinate is positive, the point to be plotted will be in quadrant _____. A I B I & II C I & IV D II

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If the x - coordinate is positive and the y-coordinate is negative, the point to be plotted will be in quadrant _____. A I B II C III D IV

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Point A is located at (-3, 2) True False

A

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Point A is located at (-5, 1) True False

A

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Point A is located at (-2, 3) True False

A

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Point A is located at (-2, 0) True False

A

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Function Families

A family of functions is a group of functions with shared traits. The parent function is the most basic function in a family. Return to Table of Contents

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Linear Functions The parent function for all linear functions is y = x Complete the table, plot the points and then connect them. y = x

X Y

  • 3
  • 2
  • 1

1 2 3

Put arrows at the end of the line to indicate the line goes on forever. PULL

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X Y

  • 4
  • 3
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  • 1

1 2 3 4

Absolute Value Functions Fill in the table for y = l x l Then plot the points and connect them. PULL

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PULL Quadratic Functions Complete the table for y = x2 Then plot the points and connect them

X Y

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  • 2
  • 1

1 2 3

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PULL Match the correct equation with the graphed function y = x y = x2 y = l x l

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19 The function graphed is y = x Yes No

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20 The function graphed is y = x2 Yes No

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21 The function graphed is y = l x l Yes No

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