Definition
Reflection
A reflection flips a figure across a mirror line, keeping paired points the same perpendicular distance from the line.
What it means
Imagine tracing a shape on see-through paper and folding the paper along a straight mirror line. The shape lands on the other side as a flipped copy. A point close to the line lands equally close on the opposite side, measured straight across at a right angle. The copy is the same size and shape, not stretched, slid, or turned.
Remember it
Fold on the mirror line: matching points land together.
Example
Reflect triangle A(1, 1), B(3, 1), C(2, 4) across the line x = 4. The images are A′(7, 1), B′(5, 1), and C′(6, 4). Each y-coordinate stays the same, and each new x-coordinate is equally far from 4 on the opposite side: 3, 1, and 2 units.
Watch for
A flip is a reflection only when one exact mirror line places every image point directly across from its source point at the same perpendicular distance. Sliding or turning the figure is not a reflection.
Common mix-up
A line of symmetry belongs to a figure and splits it into matching halves. A reflection is the action that maps points across a chosen line; that line does not have to be a symmetry line of the starting figure.
Exact meaning
A reflection is a rigid transformation across a line. For any point away from the line, the segment from that point to its image meets the line at a right angle, and the line cuts the segment into two equal lengths. Points on the line stay fixed. Distances and angle measures are preserved, while orientation is reversed.