The triangle XYZ is formed by the next points:
X=(2, 5) Y=(0, 2) Z=(3,1)
The transformations that have occurred in the XYZ triangle are:
1. A reflection over the x-axis.
It will result in a change on the sign of the x-coordinate, then the new coordinates are (-x, y):
X'=(-2, 5) Y'=(0, 2) Z'=(-3,1)
2. A translation of 3 units to the right and 5 units down.
Then, the new coordinates are given by (x+3, y-5)
X'=(-2+3, 5-5) Y'=(0+3, 2-5) Z'=(-3+3,1-5)
X'=(1, 0) Y'=(3, -3) Z'=(0,-4)
If you check, these are the final coordinates of the points that form the triangle X'Y'Z'.
Thus, the set of transformations that has occurred is: (x,y)→(-x+3, y-5). The answer is option A