In the diagram shown, two of the triangles represent the translation (x,y) ---> (x - 4. y + 5). What translation will take the image
back to the pre-image? Write your answer as a function (x,y)--->

The answer is C. I tried factoring the equation itself, and I got the correct answer but I noticed that it isn’t one of the options. Therefore, the options are partly factored but not completely. I decided to just eliminate each of the multiple choice options. I got C after expanding it. Firstly, we need to distribute the 3 to (x-2). This gives us (3x-6)(x-2). After that, we can use the FOIL method. 3x^2 - 6x -6x + 12 is the same as 3x^2 - 12x + 12.

In case you want to see the fully factored polynomial, I won’t explain the steps since you don’t need it here, but it’s 3(x-2)^2. This is equivalent to 3(x-2)(x-2). That’s the same as C.