Detailed definition
Understanding Reflection
A reflection flips a figure across a line, called the line of reflection. Each point of the image appears on the opposite side of that line at the same perpendicular distance as the original point.
Reflection preserves lengths and angle measures, so the image is congruent to the original. What changes is orientation: the figure becomes a mirror image rather than a turned copy.
This page keeps the line of reflection and the paired points on screen together so the flip can be justified by geometry, not just by appearance.
Key facts
Important ideas to remember
- A reflection flips a figure across a line.
- The line of reflection is the perpendicular bisector of the segment joining any point to its reflected image.
- Reflection is a rigid motion, so side lengths and angle measures are preserved.
- Orientation reverses under reflection, which is why letters and ordered shapes can look mirrored.
Where it is used
Where reflection shows up
- Use reflection when finding images across the x-axis, y-axis, y = x, or another mirror line.
- Use it in symmetry problems where a figure matches itself across a line.
- Use it in coordinate proofs that rely on equal distance from a line or on perpendicular bisector structure.
Common mistakes
What to watch out for
- Do not guess the reflected point by eye without checking equal perpendicular distance from the mirror line.
- Do not confuse reflection with rotation just because the image looks repositioned.
- Do not forget that the line of reflection sits midway between corresponding points, not on one side of them.