What set of reflections would carry hexagon abcdef onto itself?

a. y=x, x-axis, y=x, y-axis
b. x-axis, y=x, x-axis, y=x
c. y-axis, x-axis, y-axis
d. x-axis, y-axis, y-axis

option a. y=x, x-axis, y=x, y-axis.

Explanation:

1) Take a general point with coordinates (a,b)

2) Reflecting it over the line y = x translates it to (b,a)

3) Reflecting (b,a) over the x-axis translates it to (b,-a)

4) Reflecting (b,-a) over y = x translates it to (-a,b)

5) Reflecting (-a,b) over the y-axis translates it to (a,b)

Therefore, that set of reflections have translated (a,b) to the same place (a,b), concluding that that set of reflections carries the hexagon ABCDEF onto itself.