To find the point that is symmetric to the point [tex]\((7, -2)\)[/tex] with respect to the [tex]\(x\)[/tex]-axis, follow these steps:
1. Reflection across the [tex]\(x\)[/tex]-axis:
When reflecting a point across the [tex]\(x\)[/tex]-axis, the [tex]\(x\)[/tex]-coordinate remains the same, while the [tex]\(y\)[/tex]-coordinate changes sign.
Given the point [tex]\((7, -2)\)[/tex], the [tex]\(x\)[/tex]-coordinate is [tex]\(7\)[/tex] and the [tex]\(y\)[/tex]-coordinate is [tex]\(-2\)[/tex].
2. Change the sign of the [tex]\(y\)[/tex]-coordinate:
- The [tex]\(x\)[/tex]-coordinate remains [tex]\(7\)[/tex].
- The [tex]\(y\)[/tex]-coordinate changes from [tex]\(-2\)[/tex] to [tex]\(2\)[/tex].
3. Write the new coordinates:
The new coordinates after reflecting across the [tex]\(x\)[/tex]-axis are [tex]\((7, 2)\)[/tex].
Therefore, the point symmetric to [tex]\((7, -2)\)[/tex] with respect to the [tex]\(x\)[/tex]-axis is [tex]\((7, 2)\)[/tex].
