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

1. ## 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 $\displaystyle T_{1,-1} \circ D_2$.

Thanks.

2. ## 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.

3. ## 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.