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
<u>(a) y=x, x-axis, y=x, y-axis</u>
The rule of reflection y =x is:
![(x,y) \to (y,x)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28y%2Cx%29)
The rule of reflection across the x-axis is:
![(x,y) \to (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2C-y%29)
So, we have:
![(y,x) \to (y,-x)](https://tex.z-dn.net/?f=%28y%2Cx%29%20%5Cto%20%28y%2C-x%29)
The rule of reflection y =x is:
![(x,y) \to (y,x)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28y%2Cx%29)
So, we have:
![(y,-x) \to (-x,y)](https://tex.z-dn.net/?f=%28y%2C-x%29%20%5Cto%20%28-x%2Cy%29)
Lastly, the reflection across the y-axis is:
![(x,y) \to (-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28-x%2Cy%29)
So, we have:
![(-x,y) \to (x,y)](https://tex.z-dn.net/?f=%28-x%2Cy%29%20%5Cto%20%28x%2Cy%29)
So, the overall transformation is:
![(x,y) \to (x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2Cy%29)
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
Read more about reflections at:
brainly.com/question/938117