Reflections

Description

A reflection flips a shape over a mirror line. Every point on the image is the same distance from the mirror line as the corresponding point on the object, but on the opposite side.

To describe a reflection, you must state the equation of the mirror line (e.g. $y = x$, $x = 3$, $y = -1$).

Common mirror lines:

• $y$-axis: $(x, y) \to (-x, y)$
• $x$-axis: $(x, y) \to (x, -y)$
• $y = x$: $(x, y) \to (y, x)$
• $y = -x$: $(x, y) \to (-y, -x)$

Method: draw perpendiculars from each vertex to the mirror line, then mark the image the same distance on the other side.

The object and image are congruent and laterally inverted (mirror images of each other). Orientation is reversed in a reflection.

Common error: reflecting diagonally but not counting the correct perpendicular distance to the mirror line.

Links

Equation of a straight line Coordinates Translations Rotations