Question

Which of the following pairs of points is a reflection each other across the y-axis? Explain why.

A. (2, 15) and (2, -15)
B. (-8, -9) and (8, 9)
C. (12, -10) and (-12, -10)
D. (7, 3) and (3, 7)

Answer 1

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 \((-12, -10)\)**