To determine the image of the point [tex]\((-3, 6)\)[/tex] when it is reflected across the [tex]\( x \)[/tex]-axis, we need to understand the effect of reflecting a point across this axis.
When a point [tex]\((x, y)\)[/tex] is reflected across the [tex]\( x \)[/tex]-axis, its [tex]\( x \)[/tex]-coordinate remains unchanged, but the [tex]\( y \)[/tex]-coordinate changes to its negation. This means the point [tex]\((x, y)\)[/tex] will transform to [tex]\((x, -y)\)[/tex].
Let's apply this rule step-by-step:
1. The original coordinates of the point are [tex]\((-3, 6)\)[/tex].
2. Reflected across the [tex]\( x \)[/tex]-axis:
- The [tex]\( x \)[/tex]-coordinate remains the same: [tex]\(-3\)[/tex].
- The [tex]\( y \)[/tex]-coordinate is negated: [tex]\(6\)[/tex] becomes [tex]\(-6\)[/tex].
Therefore, the image of [tex]\((-3, 6)\)[/tex] when reflected in the [tex]\( x \)[/tex]-axis is [tex]\((-3, -6)\)[/tex].
Among the given choices:
A. [tex]\((-3, -6)\)[/tex]
B. [tex]\((3, 6)\)[/tex]
C. [tex]\((6, -3)\)[/tex]
D. [tex]\((3, -6)\)[/tex]
The correct answer is:
A. [tex]\((-3, -6)\)[/tex]
