My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 10th, 2009, 05:32 AM   #1
Newbie
 
Joined: Sep 2009

Posts: 5
Thanks: 0

Compass and ruler construction problem

Construct a point in the line a(line through A, B) so that it's equidistant to a given point E and given line b(line through C, D).

The figure of the problem is uploaded.

I've thought about this problem for several nights and tried several ideas. I've been a bit frustrated.
I'm not here for answers, I just wonder "Can it be solved by just compass and ruler construction?".
Please let me know if it can be solved or not.

If "yes", please don't let me know the construction steps, one or two hints are welcome, I'll learn to solve it by myself.
If "no", I can save time for other problems.

Thank you.
Attached Images
File Type: png 003.png (12.4 KB, 115 views)
 is offline  
 
September 10th, 2009, 11:02 AM   #2
Senior Member
 
Joined: Jan 2009
From: Japan

Posts: 192
Thanks: 0

Re: Compass and ruler construction problem

Yes, it is possible. I have not actually figured out how to do it. Are you familiar with constructible numbers? It's not too hard to prove that the distance along the line b at which to place the point (at the intersection of the perpendicular to b and line a) is constructible, so the point can be found using ruler and compass. That gives no guarantees it won't take hundreds of steps.
cmusick is offline  
September 12th, 2009, 03:48 AM   #3
Newbie
 
Joined: Sep 2009

Posts: 5
Thanks: 0

Re: Compass and ruler construction problem

I'm not familiar with constructible number.
Someone else tells me that it can be solved, in just 9 steps. But he didn't say too much.
Is it really like that? Is it really constructible in 9 steps? Any hints?
 is offline  
September 12th, 2009, 07:02 AM   #4
Senior Member
 
Joined: Jan 2009
From: Japan

Posts: 192
Thanks: 0

Re: Compass and ruler construction problem

Nine steps does not seem unreasonable. Here's how I would go about figuring them out:

Let your line 'b' lie along the x axis. Put the intersection of lines 'a' and 'b' at the origin (0, 0).

Call the x coordinate of point E '1', and the y coordinate 's' so that E is at (1, s).
Then call the height of line 'a' at x = s the number 'r', so that the line has equation y = rx.
Then you can find expressions for the point 'a' to be constructed: both the distance from E and the distance from the line will have forms in terms of r, s.
Construct that length along line b and go vertically to line a.
cmusick is offline  
September 13th, 2009, 10:17 PM   #5
Newbie
 
Joined: Sep 2009

Posts: 5
Thanks: 0

Re: Compass and ruler construction problem

I don't understand what's meaning of "Then call the height of line 'a' at x = s the number 'r', so that the line has equation y = rx."

Would you mind explain it with a figure?
 is offline  
September 13th, 2009, 10:46 PM   #6
Senior Member
 
Joined: Jan 2009
From: Japan

Posts: 192
Thanks: 0

Re: Compass and ruler construction problem

No more typos.
cmusick is offline  
September 14th, 2009, 03:38 AM   #7
Newbie
 
Joined: Sep 2009

Posts: 5
Thanks: 0

Re: Compass and ruler construction problem

I may understand your ideas now, but still don't understand "why should it be". I've briefly read "constructible number" in wikipedia, I think I may need more knowledge before I can really understand the "truth" behind.

Thank you very much.

btw, there's typo errors in your post.
 is offline  
September 14th, 2009, 03:49 AM   #8
Senior Member
 
Joined: Jan 2009
From: Japan

Posts: 192
Thanks: 0

Re: Compass and ruler construction problem

No more typos.
cmusick is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
compass, construction, problem, ruler



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Constructing a 20 Degree Angle using Compass and Ruler Only atharvjoshi Algebra 33 August 21st, 2017 03:53 AM
CAD construction problem IvanCAD Computer Science 1 June 18th, 2013 05:09 PM
Construction with ruler and compass silver Algebra 1 November 16th, 2010 09:09 AM
Suspended compass geometry problem kolg Geometry 5 December 31st, 2009 10:31 PM
a "carpenter's ruler"-type problem for knots ilovealgebra Real Analysis 1 April 7th, 2009 12:32 PM





Copyright © 2017 My Math Forum. All rights reserved.