To reflect a point across the [tex]\(x\)[/tex]-axis, you need to follow these steps:
1. Understand the reflection rule: When reflecting a point [tex]\((x, y)\)[/tex] over the [tex]\(x\)[/tex]-axis, the [tex]\(x\)[/tex]-coordinate will remain the same, and the [tex]\(y\)[/tex]-coordinate will change sign.
2. Start with the given point [tex]\(C(10, -10)\)[/tex]: This involves identifying its coordinates. For point [tex]\(C\)[/tex], [tex]\(x = 10\)[/tex] and [tex]\(y = -10\)[/tex].
3. Apply the reflection rule:
- The [tex]\(x\)[/tex]-coordinate remains unchanged, so [tex]\(x = 10\)[/tex].
- The [tex]\(y\)[/tex]-coordinate changes sign, so the new [tex]\(y\)[/tex]-coordinate is [tex]\(-(-10) = 10\)[/tex].
4. Write the new coordinates:
- The new coordinates for point [tex]\(C\)[/tex] after the reflection are [tex]\((10, 10)\)[/tex].
Thus, the coordinates of point [tex]\(C\)[/tex] after being reflected about the [tex]\(x\)[/tex]-axis are:
[tex]\[ x = 10 \][/tex]
[tex]\[ y = 10 \][/tex]
