Question

The following triangle CAT is transformed using a translation:
C = (0, 0)
A = (-2, 1)
T = (-1, 4)
Which could be coordinates of C'A'T' after the translation?
A. C=(0,0), A=(2,1), T=(1,4)
B. C=(2,0), A=(0,1), T=(1,4)
C. C=(0,0), A=(−1,−2), T=(−4,−1)
D. C=(−2,0), A=(−1,0), T=(−4,1)

Answer 1

From the given options the only possible coordinate of C'A'T' is option A. C=(0,0), A=(2,1), T=(1,4).

C=(0,0), A=(2,1), T=(1,4) is optained by refrecting the original triangle across the y-axis.

Answer 2

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.