To find the image of the point [tex]\((1, 2)\)[/tex] after a sequence of reflections, we will follow the steps provided:
1. Reflect the point [tex]\((1, 2)\)[/tex] about the [tex]\(x\)[/tex]-axis:
- When reflecting a point about the [tex]\(x\)[/tex]-axis, the [tex]\(x\)[/tex]-coordinate remains the same, and the [tex]\(y\)[/tex]-coordinate changes its sign.
- The reflected point will be [tex]\((1, -2)\)[/tex].
2. Reflect the new point [tex]\((1, -2)\)[/tex] about the [tex]\(y\)[/tex]-axis:
- When reflecting a point about the [tex]\(y\)[/tex]-axis, the [tex]\(y\)[/tex]-coordinate remains the same, and the [tex]\(x\)[/tex]-coordinate changes its sign.
- The reflected point will be [tex]\((-1, -2)\)[/tex].
Thus, the image of the point [tex]\((1, 2)\)[/tex] after the described sequence of reflections is [tex]\((-1, -2)\)[/tex]. Therefore, the number that belongs in the green box is:
[tex]\[ \boxed{-1} \][/tex]
