How Do You Do Translations?

Date: 12/09/2009 at 19:42:00
From: Florenza
Subject: How do you do translations

If (4,7) translates to (-3,9) what is the translated x-coordinate for
the point (10,-5)?

How do you translate?  I was never taught how to find translated
points.  I have no idea what to do to solve this problem.

Date: 12/10/2009 at 13:08:55
From: Doctor Peterson
Subject: Re: How do you do translations

Hi, Florenza.

Translation means sliding without rotation.  You can think in terms 
of first sliding it horizontally as far as needed to get the right x 
coordinate, and then sliding vertically to the desired y coordinate.

As an example, a translation that takes (2,-5) to (-3,1) has to go 
-5 units horizontally [(-3) - (2) = -5, so 5 to the left] and 6 places
vertically [(1) - (-5) = 6, so 6 up].

You can then describe this translation as subtracting 5 from x and 
adding 6 to y.  So this same translation would take the point (-1, 3) 
to [(-1) - (5), (3) + (6)] = (-6,9).

One notation for this translation is

  T
   -5,6

meaning that it adds -5 to x and 6 to y.

Does that help?

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 12/10/2009 at 19:40:09
From: Florenza
Subject: Thank you (How do you do translations)

Thank you so much that was an awesome explanation of how to translate.
I understood it right off the bat.  Thank you again for taking time
out of your day to help, I appreciate it very, very much.