All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Slope products (Posted on 2011-11-08) Difficulty: 1 of 5
It is a well known result from algebra that if two lines are perpendicular then the product of their slopes is always -1.*

Give a very simple proof that if the lines form any angle besides 90o the product of the slopes cannot be a constant.

*Assuming neither line is vertical.

See The Solution Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution | Comment 2 of 3 |
If the two lines are not perpendicular, then I can rotate them so that one line is horizontal and the other is neither horizontal nor vertical. The horizontal line has slope zero and so therefore is the product.

Now rotate the lines by some amount such that neither line is horizontal nor vertical. Clearly neither slope is zero now, and therefore neither is their product.

Since the product must be zero in one configuration and can't be zero in the other, it is not constant.

Perpendicular lines avoid this conflict because neither line can be made horizontal without the other being vertical, and so the zero slope case never "counts".

  Posted by Paul on 2011-11-08 18:56:41
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information