To determine which pairs of points are reflections of each other across the y-axis, we need to understand what it means for two points to be reflections across this axis.
For a point \((x, y)\), its reflection across the y-axis is \((-x, y)\). This means that the x-coordinate of the point changes sign while the y-coordinate remains the same.
Let's analyze each pair:
A. \((2, 15)\) and \((2, -15)\)
- The point \((2, 15)\) would reflect to \((-2, 15)\) across the y-axis, not to \((2, -15)\).
B. \((-8, -9)\) and \((8, 9)\)
- The point \((-8, -9)\) would reflect to \((8, -9)\) across the y-axis, not to \((8, 9)\).
C. \((12, -10)\) and \((-12, -10)\)
- The point \((12, -10)\) would reflect to \((-12, -10)\) across the y-axis, and indeed \((-12, -10)\) is the reflection of \((12, -10)\).
D. \((7, 3)\) and \((3, 7)\)
- The point \((7, 3)\) would reflect to \((-7, 3)\) across the y-axis, not to \((3, 7)\).
Given this analysis, the only pair that consists of points that are reflections of each other across the y-axis is:
C. \((12, -10)\) and \((-12, -10)\)