CALCULUS Understanding Its Concepts and Methods

Rectangular coordinates

To describe points in a plane, we draw
two axes: a horizontal one called the *x*-axis and a vertical one called the *y*-axis.

Given a point *P* = (*a*, *b*), the number *a* is called the *x*-coordinate
and *b* is the *y*-coordinate.

To describe objects in space, we need
three axes. These are usually labeled *x, y,* and *z*,
reading counterclockwise as you face the origin from the positive
sides of all three the axes. This is sometimes described as the right-hand rule**:** If
you curl the fingers of your right hand about the *z*-axis in a direction that
rotates from the *x*-axis
to the *y*-axis in a
counterclockwise direction, your thumb will point in the direction
of the positive *z*-axis.

Point (x,
y, z) |
Point (x,
y, z) |
Point (x,
y, z) |

- a
≤ x ≤ a |
x =
a |
x =
a |

y =
b |
- b
≤ y ≤ b |
y =
b |

z =
c |
z =
c |
- c
≤ z ≤ c |

Given a point *P* = (*a*, *b, c*), the number *a* is called the *x*-coordinate,
*b* is the *y*-coordinate,
and *c* is the *z*-coordinate.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.