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The
rectangular coordinate system
is also known as the Cartesian coordinate
system after Rene Descartes,
who popularized its use in
analytic geometry. The rectangular
coordinate system is based
on a grid, and every point
on the plane can be identified
by unique x and y
coordinates, just as any point
on the Earth can be identified
by giving its latitude and
longitude.
Locations on the grid are
measured relative to a fixed
point, called the origin,
and are measured according
to the distance along a pair
of axes. The x and
y axes are just like
the number line, with positive
distances to the right and
negative to the left in the
case of the x axis,
and positive distances measured
upwards and negative down
for the y axis. Any
displacement away from the
origin can be constructed
by moving a specified distance
in the x direction
and then another distance
in the y direction.
Think of it as if you were
giving directions to someone
by saying something like “go
three blocks East and then
2 blocks North.”
We specify the location of
a point by first giving its
x coordinate (the left
or right displacement from
the origin), and then the
y coordinate (the up
or down displacement from
the origin). Thus, every point
on the plane can be identified
by a pair of numbers (x, y),
called its coordinates.
Examples:
Sometimes we just want to
know what general part of
the graph we are talking about.
The axes naturally divide
the plane up into quarters.
We call these quadrants,
and number them from one to
four. Notice that the numbering
begins in the upper right
quadrant and continues around
in the counter-clockwise direction.
Notice also that each quadrant
can be identified by the unique
combination of positive and
negative signs for the coordinates
of a point in that quadrant.
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