# What is the standard definition of transforms T_{1,-1} and D_2

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• Mar 18th 2013, 05:47 AM
mathDad
What is the standard definition of transforms T_{1,-1} and D_2
What is the standard definitions of the following transforms? I got them from a practice test for the NY Regents. The test does not include those definitions in its reference sheet.

1. \$\displaystyle T_{1,-1}\$
2. \$\displaystyle D_2\$

I need this for the following:
Triangle ABC has vertices A(5,1), B(1,4), and C(1,1). What are the coordinates of triangle A''B''C'', the image of triangle ABC following composite transformation \$\displaystyle T_{1,-1} \circ D_2\$.

Answer: A''(11,1), B''(3,7), and C''(3,1).
Thanks.
• Mar 18th 2013, 07:10 AM
johng
Re: What is the standard definition of transforms T_{1,-1} and D_2
I'd say the NY regents need a copy editor. However, my initial guess was \$\displaystyle T_{a,b}\$ is translation by (a,b):
\$\displaystyle T_{a,b}\> (x,y)=(x+a,y+b).\$
Next guess was \$\displaystyle D_k\$ is central dilation by k about the origin:
\$\displaystyle D_k(x,y)=(kx,ky)\$

Apparently, from the answer, my guesses were "correct". Guessing games have no place in a math test.
• Mar 18th 2013, 11:14 AM
mathDad
Re: What is the standard definition of transforms T_{1,-1} and D_2
Agree on the copy editor and guessing remark. The sample test was off of their website, so it was probably an official past test.