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 (a) y=x, x-axis, y=x, y-axis would carry the hexagon onto itself
First; we test the given options, until we get the true option
(a) y=x, x-axis, y=x, y-axis
The rule of reflection y =x is:
[tex](x,y) \to (y,x)[/tex]
The rule of reflection across the x-axis is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex](y,x) \to (y,-x)[/tex]
The rule of reflection y =x is:
[tex](x,y) \to (y,x)[/tex]
So, we have:
[tex](y,-x) \to (-x,y)[/tex]
Lastly, the reflection across the y-axis is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex](-x,y) \to (x,y)[/tex]
So, the overall transformation is:
[tex](x,y) \to (x,y)[/tex]
Notice that, the original and final coordinates are the same.
This means that:
Reflections (a) y=x, x-axis, y=x, y-axis would carry the hexagon onto itself
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