The nice thing about this problem is that they only asked for the x coordinate of A', so we only have to follow the one point A(2, −2) through both transformations. B and C never matter here.
First the reflection across the y axis. The y axis is the vertical line, so reflecting across it flips a point left to right while leaving its height alone. In coordinates that means the x changes sign and the y stays the same:
(x, y) becomes (−x, y) Rule for a reflection across the y axis
A(2, −2) becomes (−2, −2) The 2 turns into −2, the −2 stays
Now the dilation by a factor of 3 with the origin as the center. A dilation centered at the origin just multiplies both coordinates by the scale factor, because it stretches every point straight away from the origin:
(x, y) becomes (3x, 3y) Rule for a dilation of 3 about the origin
(−2, −2) becomes (−6, −6) Multiply both coordinates by 3
So A' is (−6, −6) and the x coordinate is −6, which is answer B.
Two things worth keeping in mind on problems like this one. The order matters, so do the transformations in the order the problem gives them, and remember that a dilation about the origin multiplies the coordinates while a reflection only changes a sign.
Also notice that the answer choices are built out of the common mistakes. You get −4 if you forget to dilate and just double something, and you get 2 if you skip the reflection and only look at the sign of the original point, so seeing your answer in the list does not by itself mean you did it right.
