Answer: option D) y=x, x-axis, y=x, y-axis.
I first thought it was the option C) and I tried with it but it was wrong. This is how I dit it.
Option C step by step:
1) Reflection over the x - axis => point with coordinates (a,b) is transformed into point with coordinates (a, -b)
2) Reflection over the line y = x => point with coordinates (a, -b) is transformed into point with coordinates (-b,a)
3) New feflection over the x - axis => (-b,a) transforms into (-b, -a)
4) New reflection over the line y = x => (-b,-a) transforms into (-a,-b)
Which shows it is not the option C).
Then I probed with option D. Step by step:
1) Reflection over the line y = x => (a,b) → (b,a)
2) Reflection over the x-axis => (b,a) → (b,-a)
3) Reflection over the line y = x => (b,-a) → (-a,b)
4) Reflection over the y-axis => (-a,b) → (a,b).
So, this set of reflections, given by the option D) transforms any point into itself, which proofs that the option D) is the right answer.
