To determine the reflection of the point [tex]\((-7, 1)\)[/tex] across the origin, follow these steps:
1. Understand Reflection Across the Origin:
When a point [tex]\((x, y)\)[/tex] is reflected across the origin, its coordinates are transformed to [tex]\((-x, -y)\)[/tex]. This means both the [tex]\(x\)[/tex]-coordinate and the [tex]\(y\)[/tex]-coordinate change their signs.
2. Apply the Transformation:
- For the point [tex]\((-7, 1)\)[/tex]:
- The [tex]\(x\)[/tex]-coordinate is [tex]\(-7\)[/tex]. When reflected across the origin, it becomes [tex]\(-(-7)\)[/tex] which is [tex]\(7\)[/tex].
- The [tex]\(y\)[/tex]-coordinate is [tex]\(1\)[/tex]. When reflected across the origin, it becomes [tex]\(-(1)\)[/tex] which is [tex]\(-1\)[/tex].
3. Combine the Transformed Coordinates:
Therefore, the point [tex]\((-7, 1)\)[/tex] when reflected across the origin, maps onto [tex]\((7, -1)\)[/tex].
Thus, the correct answer is:
A) [tex]\((7, -1)\)[/tex]
