# Composite Transformation

1. Jan 12, 2010

### golb0016

1.) If (-4,8) is the image under the composite transformation Th,3 x T-2,k(-3,0), what are the coordinates of the image of (2,-1) under the same composite transformation?

3. The attempt at a solution

I'm lost on this one.

2. Jan 12, 2010

### HallsofIvy

Staff Emeritus
I assume that "Th,3" is translation by "h" in the x direction and "3" in the y direction- that is, that Th,3(x, y)= (x+h, y+3)- and that "T-2, k" is translation by "-2" in the x direction and "k" in the y direction- that is, that T-2,k(x,y)= (x-2, y+ k).

If that is so then Th,3 x T-2,k(-3, 0)= Th,3(-3-2, 0+k)= Th,3(-5,k)= (-5+h, 3+k)= (-4,8). That is, -5+h= -4 and 3+ k= 8. Now, what are h and k? Once you know that, finding Th,3x T-2,k(2, -1) should be easy.