Reflection

A reflection flips a shape across a mirror line. Each point maps to a new point the same perpendicular distance on the other side of the mirror line — so the mirror line is the perpendicular bisector of every segment joining a point to its image.

The shape keeps its size and its angles, but its orientation is reversed: the image is a mirror image, as if you had turned the shape over. Lengths and angles are unchanged — only the handedness flips.

Reflection in coordinates

On a grid, reflecting in the common mirror lines is just a sign-swap or a swap of coordinates:

in the x-axis: (x, y) \mapsto (x, -y);
in the y-axis: (x, y) \mapsto (-x, y);
in the line y = x: (x, y) \mapsto (y, x).

Seeing it on a grid

Take the triangle with vertices (1, 1), (3, 1) and (1, 4), and reflect it in the line y = x. Step through the figure: each vertex swaps its coordinates, so the image has vertices (1, 1), (1, 3) and (4, 1) — same size, same angles, reversed orientation.