graph and can be a combination of two numbers for a two-dimensional figure or three
numbers for three dimensions.
How are two-dimensional Cartesian coordinatesdetermined?
With two-dimensional Cartesian coordinates (or rectangular coordinates), an
ordered pairof two numbers is determined using two axes oriented perpendicular
to each other (for more about ordered pairs, see “Foundations of Mathematics”).
The ordered pair coordinates are found by specifying points along the two axes:
First, along the x-axis, the positive or negative amount on either side of the y,or
vertical, axis; this is called the abscissaand indicated as x. The other number is the
positive or negative amount on either side of the x,or horizontal, axis; this is called
the ordinateand indicated as y. The coordinates are usually written in terms of x
and yat the point as an ordered pair; for example, in the illustration of a two-
dimensional coordinate system on p. 194, the ordered pair is (7, 8), in which xis 7
and yis 8.
What are quadrants?
Graphs used in the Cartesian coordinate system are broken down into quadrants, or
four segments. For example, in a two-dimensional system, the xand yaxis—with the
origin as zero and the two axes perpendicular to each other—form the four quadrants.
In the top left quadrant (quadrant II), the xis negative and the yis positive; in the top
right quadrant (quadrant I), both coordinates are positive; in the bottom left quadrant
(quadrant III), Cartesian coordinates are both negative; and in the bottom right quad-
rant (quadrant IV), the xis positive and the yis negative. 193
GEOMETRY AND TRIGONOMETRY
Who developed analytic geometry?
A
nalytic geometry began when French philosopher, mathematician, and sci-
entist René Descartes (1596–1650; in Latin, Renatus Cartesius) published a
work explaining how to use coordinates for finding points in space. He was the
first to make a graph and presented a geometric interpretation of a mathemati-
cal function; this marked a step toward what is now known as Cartesian coordi-
nates, a term derived from Descartes’s Latin name. Around the same time—and
independently—French mathematician Pierre de Fermat (1601–1665) also did
much to establish the ideas of coordinate geometry. But, unlike Descartes, Fer-
mat did not publish his work. Both Descartes’s and Fermat’s ideas would lead to
modern Cartesian coordinates. (For more about Descartes and Fermat, see “His-
tory of Mathematics.”)