SECTION
11.1: THE ORIGIN OF THE CARTESIAN COORDINATE SYSTEM
The year is 1630. Lying on his back, French mathematician René Descartes(pronounced "daycart") watched a fly crawl across the ceiling. Suddenly, an idea came to him.
Descartes visualized two number lines intersecting at a 90° angle. He realized that he could determine the fly's location on a piece of paper. Descartes called the horizontal line the xaxis and the vertical line the yaxis. He named the point where the axes intersect at 90 degrees the origin. He then placed "tic marks" evenly spaced along the vertical and horizontal axes, and assigned positive and negative numbers to those tic marks.
Descartes decided to represent the fly's location as an ordered pair of numbers. The first number of the ordered pair, the xvalue, is the horizontal distance along the xaxis, measured from the origin. The second number of the ordered pair, the yvalue, is the vertical distance along the yaxis, also measured from the origin. The locations in the plane where the x and y values intersect are called coordinates. There is an xcoordinate and there is a ycoordinate which are grouped together in parentheses and seperated by a comma. The xcoordinate always comes first in this grouping and the ycoordinate always follows the xcoordinate in this grouping. This grouping of two numbers seperated by a comma and paced in parentheses is called an "ordered pair."
The Cartesian Coordinate System
The fly's position above is represented by the ordered pair of numbers (5, 4) made up of the xcoordinate, 5, and the ycoordinate, 4. You can say the fly is at a point represented by the ordered pair (5, 4). The plane above containing the ordered pair (5, 4) is called the "Cartesian Coordinate System," or the "Coordinate Plane."
The Cartesian Coordinate System is divided in 4 regions called "quadrants." The fly above is in quadrant 4. It is important that you are able to tell someone what quadrant in which a point sits. The graph below contains 9 points labeled with their respective ordered pairs. Once you read the rules on determing what quadrant a point sits in you will easily be able to determine what a quadrant a point is in.
RULES FOR DETERMINING WHICH QUADRANT A POINT IS IN 
RULE 1) Any point on the x or y axis is said to "not be in a quadrant."
ex. In the graph below, the points defined by the ordered pairs (0,4), (6,0), (0,0), (4,0) and (0,3) are not in any quadrant.
RULE 2) QUADRANT 1 Where the x and y coordinate are both positive
ex. In the graph below, the point defined by the ordered pair (3,2) is in quadrant 1
RULE 3) QUADRANT 2  Where the x coordinate is negative and the y coordinate is positive
ex. In the graph below, the point defined by the ordered pair (2, 3) is in quadrant 2
RULE 4) QUADRANT 3  Where the x coordinate is negative and the y coordinate is negative
ex. In the graph below, the point defined by the ordered pair (4, 2) is in quadrant 3
RULE 5) QUADRANT 4  Where the x coordinate is positive and the y coordinate is negative
ex. In the graph below, the point defined by the ordered pair (5, 4) is in quadrant 4

YOU MUST KNOW HOW TO USE THE FOLLOWING LANGUAGE 
1) Cartesian Coordinate System or Coordinate Plane
2) vertical axis and horizontal axis
3) tic marks, also called hash marks
4) origin
5) xaxis, positive xaxis, and negative xaxis
6) yaxis, positive yaxis, and negative yaxis
7) quadrant I, quadrant II, quadrant III, and quadrant IV
8) tic and hash marks
9) ordered pair, xvalue, yvalue, coordinate(s), xcoordinate, ycoordinate, and point

In the next chapter we will look more fully at the use of the above language and the Cartesian Coordinate System.



THE SUMMER STUDY GUIDE
BY CHAPTERS

RETURN TO THE SUMMER STUDY GUIDE MAIN PAGE
 CHAPTER 1: THE NUMBER SYSTEM
 CHAPTER 2: ORDER OF OPERATIONS
 CHAPTER 3: VARIABLES, MONOMIALS,
BINOMIALS, TRINOMIALS, POLYNOMIALS,
COEFFICIENTS, TERMS AND LIKE TERMS
 CHAPTER 4: SIGNED NUMBERS,
ABSOLUTE VALUE, AND INEQUALITY SYMBOLS
 CHAPTER 5: FACTORS, COMMON
FACTORS, LEAST COMMON FACTORS AND GREATEST COMMON FACTORS
 CHAPTER 6: PROPERTIES OF NUMBERS
 CHAPTER 7: THE WORLD OF FRACTIONS
 CHAPTER 8: EXPONENTS
 CHAPTER 9: ROOTS
 CHAPTER 10: ALGEBRAIC EXPRESSIONS
 CHAPTER 11: CARTESIAN COORDINATE SYSTEM
 CHAPTER 12: SETS, RELATIONS AND FUNCTIONS
 CHAPTER 13: AVERAGE RATE OF CHANGE OF Y WITH RESPECT TO X, SLOPE, PYTHAGOREAN THEOREM, AND DISTANCE FORMULA BETWEEN TWO POINTS
 CHAPTER 14: XINTERCEPT(ZERO) AND Y INTERCEPT(B)
 CHAPTER 15: LINES
 CHAPTER 16: FUNCTIONS
 CHAPTER 17: MULTIPLYING POLYNOMIALS
 CHAPTER 18: FACTORING
 CHAPTER 19: RATIONAL EXPRESSIONS
 CHAPTER 20: SOLVING EQUATIONS
 CHAPTER 21:SOLVING INEQUALITIES
 CHAPTER 22: SOLVING A SYSTEM OF EQUATIONS
 CHAPTER 23: QUADRATICS
 CHAPTER 24: CIRCLES
 CHAPTER 25: AREAS AND PERIMETERS OF PLANE FIGURES
 CHAPTER 26: VOLUMES
