To find the mirror image of a point [tex]\((x, y)\)[/tex] across the [tex]\(y\)[/tex]-axis, we need to understand that reflecting over the [tex]\(y\)[/tex]-axis changes the sign of the [tex]\(x\)[/tex]-coordinate while keeping the [tex]\(y\)[/tex]-coordinate unchanged.
Let's examine the point [tex]\((-7, 10)\)[/tex]:
1. Original Point:
[tex]\[
(x, y) = (-7, 10)
\][/tex]
2. Reflection over the [tex]\(y\)[/tex]-axis:
- The [tex]\(x\)[/tex]-coordinate of the point will change from [tex]\(x = -7\)[/tex] to [tex]\(x = 7\)[/tex]. This is because reflection over the [tex]\(y\)[/tex]-axis negates the [tex]\(x\)[/tex]-coordinate.
- The [tex]\(y\)[/tex]-coordinate will remain the same at [tex]\(y = 10\)[/tex].
As a result, the new coordinates after reflecting over the [tex]\(y\)[/tex]-axis are:
[tex]\[
(7, 10)
\][/tex]
Thus, the mirror image of the point [tex]\((-7, 10)\)[/tex] in the [tex]\(y\)[/tex]-axis is [tex]\((7, 10)\)[/tex].
