When a set of reflections that carry a shape onto itself, it means that the final position of the shape will be the same as its original location

Reflections <em>(a) y=x, x-axis, y=x, y-axis </em>would carry the hexagon onto itself

First; we test the given options, until we get the true option

The rule of reflection y =x is:

$(x,y) \to (y,x)$

The rule of reflection across the x-axis is:

$(x,y) \to (x,-y)$

So, we have:

$(y,x) \to (y,-x)$

The rule of reflection y =x is:

$(x,y) \to (y,x)$

So, we have:

$(y,-x) \to (-x,y)$

Lastly, the reflection across the y-axis is:

$(x,y) \to (-x,y)$

So, we have:

$(-x,y) \to (x,y)$

So, the overall transformation is:

$(x,y) \to (x,y)$

Notice that, the original and final coordinates are the same.

This means that:

Reflections <em>(a) y=x, x-axis, y=x, y-axis </em>would carry the hexagon onto itself