Consider options A and C. In these options point C stays stationary, this means that points A and T should stay stationary too. But it is not so.
Options A and C are false.
Consider option B:
- C(0,0)→C'(2,0) {here the translation is (x,y)→(x+2,y)}
- A(-2,1)→A'(0,1) {here the translation is (x,y)→(x+2,y)}
- T(-1,4)→T'(1,4) {here the translation is (x,y)→(x+2,y)}
As you can see made translation is the same for all three points, then option B is correct.
Consider option D:
- C(0,0)→C'(-2,0) {here the translation is (x,y)→(x-2,y)}
- A(-2,1)→A'(-1,0) {here the translation is (x,y)→(x+1,y-1)}
- T(-1,4)→T'(-4,1) {here the translation is (x,y)→(x-3,y-3)}
As you can see made translation is not the same for all three points, then option D is false.
Answer: correct choice is B.