## Saturday, January 26, 2013

When thinking of the rectangular coordinate system, imagine a city that is set up with all streets running north to south and east to west. The streets running north to south are equal distance and parallel to each other as are the streets running east to west. Drawing the streets on the graph would show a grid with equal sized squares. In algebra, the vertical (north to south) line straight through the middle of the is known as the y-axis and the horizontal (east to west) line straight through the middle is known as the x-axis. The center of the graph is known as the origin.

There are four sections of the rectangular coordinate system created by the intersection of the x and y axis. Each section is known as a quadrant. It's easy to remember by thinking of "quad", which means four. The quadrants are named I, II, III and IV, starting in the upper right and rotating counter clockwise.

Think of the layout of a city. The north to south streets start at 1 and go to 10 and are avenues. The east to west streets start at 1 and go to 10 and are boulevards. Suppose John lives at the intersection of East 5th Boulevard and North 8th Aenue and Susie lives at the intersection of West 6th Boulevard and South 2nd Avenue. You can plot John's location on the graph by staring at the origin, moving right to East 5th boulevard and then up to North 8th street. Likewise, you can plot Susie's location by starting at the origin and moving left to West 6th boulevard and South to 2nd street. Notice how John's location is labeled as (5, 8) in the following graph. This point is called an ordered pair. Each number in the ordered pair is known as a coordinate.

The first number in an ordered pair is the x- coordinate and the second number in an ordered pair is the ycoordinate. Note that a coordinate is in the form (x, y). Coordinates on the x-axis are negative left of the origin and positive right of the origin. Coordinates on the yaxis are negative below the origin and positive above the origin. The coordinate of the origin is (0,0) since it is the middle of the graph. From this information, we can tell what quadrant a point falls. If both coordinates are positive, the point falls in the first quadrant. If both coordinates are negative, the point falls in the third quadrant. If x is negative and y is positive, the point falls in the second quadrant. If x is positive and y is negative, the point falls in the fourth quadrant.

Examples:
(-2, 4) falls in the second quadrant.
(4, 10) falls in the first quadrant.
(-8, -3) falls in the third quadrant.
(9, -6) falls in the fourth quadrant

This guide should provide a good introduction and ease any confusion about the rectangular coordinate system.