Saturday, March 31, 2007

Graphing - Points, Ordered Pairs

The first graphing concept to understand is x-y coordinates. A POINT has both an x-coordinate AND a y-coordinate. The x-coordinate is how far left/right the point lies, and the y-coordinate is how far up/down. A single point is determined by both how far left/right and up/down it is. Together, the x- and y-coordinates of a point are called an ORDERED PAIR. Every point is represented by a different ordered pair. (If they were the same, they'd be in the same place!) The standard way of writing an ordered pair is (x,y). Also, the point itself is often named with a letter and placed before the ordered pair... like M(x,y) for point M that has x- and y-coordinates.

Refer to this graph for the following examples

So, for point S with x=3 and y=5 , it will be written as S(3,5) and will be 3 units to the right and 5 units up.

For point T with x=(-2) and y=1, it will be written as T(-2,1) and will be 2 units to the left (pay attention to the negative sign) and 1 unit up.

Point U(-4,-4) is 4 units left and 4 units down (two negative signs this time).

V(2,-5) is 2 units right and 5 units down.

Try for yourself... where would you draw points (1,1) and (-5,7)? What about the two points on the graph that don't have any labels... can you figure out what they should be? Let's call the point on the right W, and the point on the left N. Easy, right? They are W(8,1) and N(-8,7)! All you have to do is count in the proper direction, and you know where your point goes and what its coordinates are! Once you are familiar with how points are labeled and how their positions are calculated, you will be able to work with these numbers to do all sorts of things!

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