Final answer:
To find the combined transformation of the point A(4,5) under reflections F and G, first find the image of A under F and then the image of that point under G. The final image of point A under FOG is (-4,5).
Step-by-step explanation:
To find the combined transformation of the point A(4,5) under the reflections F and G, we need to first find the image of point A under F, and then find the image of that point under G.
Reflection on the line x=2 means that we mirror the point across the line x=2. Since the x-coordinate of point A is 4, the image of A under F will have an x-coordinate of 2- (4-2)= 0.
Now, we apply the reflection on the line x=-2 to the image obtained from the previous step. Since the x-coordinate of the image is 0, the image under G will have an x-coordinate of -2- (0-(-2))= -4. So the final image of point A under FOG is (-4,5).