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 March 1st, 2013, 02:29 PM #1 Member   Joined: Aug 2012 Posts: 71 Thanks: 1 Geometry problem I am really stuck on this problem. Q. A person plans a walking track to a tree, located at the point (20,36) on a map. The nearest road to the tree has equation 2x + 7y = 35 He draws the track to the tree from this road on the map, so that the track is as direct as possible. What is the equation of the line that he has drawn? This is my answer: y= 2x-4 Thanks for your help
March 1st, 2013, 04:19 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: How to solve...

Hello, Doc!

Did you make a sketch?

Quote:
 A person plans a walking track to a tree, located at the point (20,36) on a map. The nearest road to the tree has equation $2x\,+\,7y\:=\:35.$ He draws the track from the road to the tree so that the track is as short as possible. What is the equation of the line that he has drawn?

Code:
      |                T
|               o(20,36)
Ao              *
|   *         *
|       *    *
|           o
|          P    *
|                   *
|                       oB
- + - - - - - - - - - - - - -
|
$\text{The tree is at }T(20,\,36)$

$\text{The road is }AB\text{ with the equation: }\,y \:=\:-\frac{2}{7}x\,+\,5$

$\text{The track will be from }T\text{ to }P\text{, where }TP \,\perp\,AB.$

$\text{The track will contain }(20,36)\text{ and have slope }\frac{7}{2}$

$\text{Its equation is: }\:y\,-\,36 \:=\:\frac{7}{2}(x\,-\,20) \;\;\;\Rightarrow\;\;\; y \:=\:\frac{7}{2}x\,-\,34$

Last edited by skipjack; January 8th, 2015 at 12:26 PM.

 March 1st, 2013, 06:25 PM #3 Member   Joined: Aug 2012 Posts: 71 Thanks: 1 Re: Geometry problem Thanks very much! I really struggle with maths.
 January 4th, 2015, 09:18 PM #4 Newbie   Joined: Jan 2015 From: Pakistan Posts: 1 Thanks: 0 Just wanted some help with answering this past exam paper. Can you provide some solutions please and the steps involved in getting there?
 January 4th, 2015, 09:30 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Post a new thread containing your problem (soroban's explanation should suffice here). Last edited by greg1313; January 4th, 2015 at 10:01 PM.
 January 5th, 2015, 12:31 AM #6 Senior Member     Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry The nearest way is the perpendicular line from tree to road.

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