Reflect a Point Across an Axis

Reflecting a Point Across an Axis

1. Identify the axis
   Find whether the point is reflected across the x-axis or the y-axis. The axis tells you which coordinate stays the same and which one changes.

2. Use the reflection rule

   • Across the x-axis: keep the x-coordinate, change the sign of the y-coordinate.
     Example: ((x, y) \to (x, -y))
   • Across the y-axis: keep the y-coordinate, change the sign of the x-coordinate.
     Example: ((x, y) \to (-x, y))

3. Write the new point carefully
   Copy the unchanged coordinate exactly and only switch the sign of the coordinate that moves to the opposite side of the axis. Be careful with negative numbers: changing the sign of a negative number makes it positive.

4. Check your answer
   The reflected point should be the same distance from the axis as the original point, but on the opposite side. If the axis is the x-axis, both points should have the same x-value. If the axis is the y-axis, both points should have the same y-value.

Quick self-check

• Did only one coordinate change?
• Did you simplify the final answer?
• Is the image mirrored correctly across the axis?