Math 1090-001 (Spring 2001)
The Cartesian Plane
Friday Jan 12, 2001 1
The Cartesian Plane is a standard graphical representation of
๎
2, the set of ordered pairs of real numbers.
โขThe Cartesian Plane has a pair of mutually perpendicular coordinate axes. Usually, these two axes are drawn
horizontally and vertically as in the diagram below.
โขThe point of intersection of these two axes is called the origin.
โขThe arrow on each axis indicates the direction of increase of the coordinate of that axis. Usually we give names
to the axes. For the discussion below, we will call the horizontal axis the x-axis and the vertical one the y-axis.
โขEach point in the Plane determines an ordered pair of real numbers and vice versa as follows:
1. Suppose a point Pon the plane is given.
2. Draw a horizontal and vertical line through P.
3. Denote the intersection of this horizontal line with the y-axis (the vertical axis) by Band denote the inter-
section of the vertical line with the x-axis (the horizontal axis) by A.
4. We now define the y-coordinate, denoted by yP, of the point Pto be the signed distance from the origin to
the point A. Similarly, we define the x-coordinate, denoted by xP, of Pto be the signed distance from the
origin to the point B. (See the diagram below.)
5. Now, we associate to the point Pโ which is in the Cartesian Plane โ to the ordered pair (xP, yP) of real
numbers.
6. Conversely, given any ordered pair (a, b), we assoicate to it the point in the Plane with x-coordinate aand
y-coordinate b.
x
6
y
-
๎
Pโ(xP, yP)
A
๎
B
๎
xP>0-
0< yP
6
๎
(โ3,โ2)
๎
(2,4)
๎
(โ4,3)
๎
(3,โ3)
