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					Subtracting Coordinates

There are three steps to playing this game.
   1. Determine your current position (coordinates in your first ordered pair)
   2. Determine where you want to move (coordinates of your second ordered pair)
   3. Determine what horizontal and vertical movement Plotter needs to make to move
       to a fish. Slide the x and y sliders to move Plotter in the direction and distance he
       needs to go.”

What is An Ordered Pair:
   An ordered pair has two numbers separated by a comma inside of parentheses, like
this (0, -5). These tell us where a point is on a graph. In an ordered pair, the first
coordinate, the number on the left, represents the value along the x-axis. It is called the
x-coordinate. The second coordinate, the number on the right, represents the value along
the y-axis. It is called the y-coordinate. Coordinates can be positive or negative numbers.

Example: The ordered pair (2, 6) represents a point that has an x-coordinate of 2 and a y-
coordinate of 6.

Determining Ordered Pairs (Your current position or your desired position)
   There are two number lines on a coordinate graph. One is on the x-axis (horizontal)
and one is on the y-axis (vertical). They cross at zero.

   Figure out where Plotter Penguin is standing on the graph. The penguin is standing on
an intersection of two lines (where the two lines cross). Look at the horizontal number
line (x-axis). Figure out what number Plotter is standing under or over. That is the first
number of Plotter’s position (the x-coordinate). Then look at the vertical number line.
Figure out what number is to Plotter’s right or left. That represents the second number of
Plotter’s position (the y-coordinate).

    Let’s say Plotter is standing over the – 3 of the horizontal axis and to the left of the 4
on the vertical axis. So he is standing at a point that has the x-coordinate of – 3 and the
y-coordinate of 4. We can state this by the ordered pair (- 3, 4).
Positive Directions on the X and Y Axis

   Moving to the right on the x-axis is moving positively because the numbers get bigger
as you move to the right. Don’t be fooled by negative numbers on your x-axis.
Remember that – 3 is LESS than – 1. Moving to the left on this axis is moving
negatively, of course.

   Moving upward on the y-axis is moving positively because the numbers on that
number line get larger as you move up the axis. Moving downward on this axis is
negative movement. Again, don’t let those negative numbers on the number line fool you.

Moving From One Point to Another

   Once you have two ordered pairs (where Plotter starts and where you want him to end
up), you can figure out how to get the penguin from place to place. This can be done by
subtracting the x-coordinates and then subtracting the y-coordinates. The result tells you
how far to move on each axis.

   In this example, Plotter started on (– 3, 4) and wants to move to a point (1, 5). You
can see this on the graph below. The dotted lines indicate the movement. Note: Plotter
can only move in a horizontal and/or vertical direction. Plotter cannot move diagonally.
Plotter will move on the x-axis a distance of 4 units ( from –3 to –2, -1, 0, 1) in a positive
direction and on the y-axis a distance of 1 unit (from 4 to 5) in a positive direction. If
you count the intersections, you can see this.
Though you can count it out using the graph, you can also figure it out using subtraction.
Start with the ordered pair of the place you want to move to and subtract the ordered pair
of the place you started. For instance, Plotter is starting at (-3, 4) and wants to go to (1,
5). Plotter wants to go to the x-coordinate (1) , so subtract the x-coordinate where he
started (- 3).
                                     1 – (- 3) = 4
This tells you how to move on the x-axis. You will move 4 units horizontally in the
positive direction.

Then Plotter wants to go to the y-coordinate (5), so subtract his current y-coordinate of 4.
This tells you how to move on the y-axis. You will move 1 unit vertically in the positive

If your answer was a negative number, you would have to move in the negative direction
on that axis.

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