Final answer:
The length of XZ is 42 units.
Step-by-step explanation:
In the given problem, triangle QRS maps to triangle XYZ with a transformation (X,Y) -> (6X, 6Y). We are given that QS = 7 and we need to find the length of XZ.
Since the transformation multiplies the x-coordinate and y-coordinate of a point by 6, the side lengths of triangle XYZ are 6 times the corresponding side lengths of triangle QRS. Therefore, if QS = 7, then XZ = 6 * 7 = 42.