1.2 Lines in the Plane

 

Summary

A line is one of the most important geometric objects for representing points in the plane. We shall also see later that, much like the experience we have when zooming in, many curves in the plane are approximately linear in small regions. In this section we learn how to recognize a line from its equation, and we learn how to write the equation of a line from information about it.

By the end of your studying, you should know:

On-screen applet instructions: Move the sliders and describe the effect.

Examples

Let L1 be the line ax + by = c, where a, b, and c are constants. What is the equation of the line perpendicular to L1, passing through the point (0, c)?

Find the equation of a line through (1, 1) perpendicular to a line passing through (1, 2) and (3, 5).

Consider a triangle with vertices (1, 1), (9, 7), and (3, 11). Do the perpendicular bisectors of the sides of the triangle intersect in a single point?

Videos

See short videos of worked problems for this section.

Quiz

Take a quiz.

Exercises

See Exercises for 1.2 Lines in the Plane (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

Resources on the Web

Information on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"

Information on Leibniz
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"

Calculus Applications
Project Intermath

Plane Division by Lines
Wolfram Research

Interesting Application

Do you see lines in the waves?

1.1 Modeling Discrete Data Table of Contents 1.3 Functions and Their Graphs


Software requirements: For best results viewing and interacting with this page, get the free software listed here.

Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel