To find the image of the point [tex]\((-3,4)\)[/tex] when it is reflected across the [tex]\(y\)[/tex]-axis, follow these steps:
1. Understand the Reflection Across the [tex]\(y\)[/tex]-axis:
Reflecting a point across the [tex]\(y\)[/tex]-axis involves changing the sign of the [tex]\(x\)[/tex]-coordinate while keeping the [tex]\(y\)[/tex]-coordinate the same.
2. Apply the Reflection Rule:
- The original point is [tex]\((-3, 4)\)[/tex].
- To reflect this point across the [tex]\(y\)[/tex]-axis, we change the sign of the [tex]\(x\)[/tex]-coordinate:
[tex]\[
x = -3 \rightarrow -x = -(-3) = 3
\][/tex]
- The [tex]\(y\)[/tex]-coordinate remains unchanged:
[tex]\[
y = 4
\][/tex]
3. Determine the Reflected Point:
Therefore, the coordinates of the reflected point are:
[tex]\[
(3, 4)
\][/tex]
So, the image of the point [tex]\((-3, 4)\)[/tex] when reflected across the [tex]\(y\)[/tex]-axis is [tex]\((3, 4)\)[/tex].
The correct answer is:
[tex]\[
(3, 4)
\][/tex]
