Linear Transformations

Date: 6/13/96 at 18:2:58
From: ourpond
Subject: Linear transformations

Dear Dr. Math,

I'm having a problem with this question. If you could help me that 
would be great!

Determine the image of (2,-6) under (x,y) ---> (x+3, y+5)

Thanks. Tanya

Date: 6/14/96 at 8:59:53
From: Doctor Patrick
Subject: Re: Linear transformations

Hi Tanya!  This problem is what is known as a transformation.  You 
take your starting point (or points) and perform the changes required 
in order to find a new image.
  
In this case, we are told that any point (x,y) will be changed to 
(x+3, y+5).  Since (2,-6) names a point where x = 2 and y = -6, 
we can use the formula we were given to find a new point.  

Since x becomes x+3, in this example where x = 2, our new x value will 
be 2+3, or 5.

Now we do the same thing for the y value.  y = -6 in this problem, and 
y needs to be transformed to y+5.  What do you think the new y value 
will be?

I'll let you figure out that part on your own.  The last step is to 
put the two parts together in (x,y) form with the new values.  

Good luck,

-Doctor Patrick,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/