Pre Algebra (Period 2 & 4)

Coordinate Graphing 1-10

Review of the xy coordinate plane.


Cartesian plane:
Named after French mathematician Descartes.

plane: a two dimensional (across and up/down) flat surface that extends infinitely in all directions.



quadrant: 2 perpendicular lines called axes split the plane into 4 regions....quad means 4

quadrant names: begin in the top right (where you normally write your name!) and go counterclockwise in a big "C" (remember it for "C"oordinate)

They are named I, II, III, IV in Roman Numerals


coordinate - A coordinate is the position of a point in the Cartesian plane


coordinate = "co" means goes along with (coworker, co-president, co-champions)

"ordinate" means in order

So coordinate means numbers that go along with each other in a certain order

The numbers are the x and y values and the order is that the x always comes first


Also called an ordered pair (x y order and pair of numbers)

Ordered pairs are recognized by the use of ( x , y ) format



origin = (0, 0) the center of the graph (its beginning or origin)

When you count the coordinate' s position, you count from the origin.


x comes before y in the alphabet so the order is (x, y) ....
always go right or left first, then up or down


the x axis is the horizontal axis (goes across)


Remember that because the number line also is horizontal and you learn that first 
(the pattern to remember is x is always first and the number line is before going up and down)


NOW LET'S GET TO WHAT YOU ACTUALLY DO TO GRAPH!!!

1) Count your x value:

positive x, count right from origin (positive numbers are to the right of zero on number line)

negative x, count left from origin

2) Count your y value:

positive y value, count up from where your x value was (up is the positive direction)

negative y value, count down from where your x value was (down is the negative direction)


EXAMPLES:

(3, 5) Count 3 to the right from the origin, then 5 up

(3, -5) Still count 2 to the right, but now count 5 down

(-3, 5) Count 3 to the left from the origin, then count 5 up

(-3, -5) Again count 3 to the left, but now count 5 down



BUT WHAT HAPPENS WHEN 
ONE OF THE VALUES IS ZERO?

If the y value is zero it means that you move right or left, but don't go up or down:

SO YOUR POINT WILL BE ON THE x AXIS........
x axis is where y = 0 

Example: (3, 0) is a point on the x axis, 3 places to the RIGHT

Example: (-3, 0) is a point on the x axis, 3 places to the LEFT



If the x value is zero it means that you don't move right or left, you just go up or down.

SO YOUR POINT WILL BE ON THE y AXIS...........
y axis is where x = 0 

Example: (0, 3) is a point on the y axis, 3 places UP

Example: (0, -3) is a point on the y axis, 3 places DOWN
Now when the question is
if x is positive and y is negative, what quadrant is it? IV
If x is positive and y is positive, what quadrant is it? I
If x is negative and y is positive, what quadrant is it? II
If x is positive and y is negative, what quadrant is it? III
These questions could be stated like this:
if x >0 and y <0 what quadrant is it? Now think: IF x > 0 it must be a positive number and if y <0 it must be a negative number.. and then use the rules above!!