Final answer:
After analyzing the provided transformation, it becomes evident that the scaling factor is 3. Thus, the length of line segment QR is one-third the length of WX, meaning QR equals 4 units.
Step-by-step explanation:
The student has provided details on a transformation that maps triangle PQR to triangle AVWX, with the function (x, y) =(x + 3, y - 1) + (2x, 2y). We can see that this transformation consists of a translation followed by a scaling. To find the length of QR, knowing that WX equals 12, we need to determine the scaling factor of the transformation.
By analyzing the transformation step by step, we can see that the transformation can be rewritten as (x', y') = (3x + 3, 3y - 1), where x' and y' are the coordinates after the transformation. This shows that the x- and y-coordinates are both multiplied by 3, indicating the scaling factor is 3.
Since WX corresponds to QR and the scaling factor is 3, the original length of QR, before the transformation, is WX divided by the scaling factor. Therefore, QR = WX / 3 = 12 / 3 = 4. This means the length of QR is 4 units.