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Reflections

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In geometry, a reflection is a transformation that flips an object across a line or plane. When an object is reflected, its image is created on the opposite side of the line or plane of reflection. The line or plane of reflection is called the "mirror line" or "mirror plane."

Reflections preserve the size and shape of an object, but they change its orientation. For example, if you were to reflect a square across a mirror line, the resulting image would be a square with the same size and shape as the original, but facing in the opposite direction.

Reflections can be depicted using matrices, which are collections of numbers that describe transformations in geometry. The matrix for a reflection across the x-axis is:

[1 0]

[0 -1]

The matrix for a reflection across the y-axis is:

[-1 0]

[ 0 1]

Reflections are helpful to understand symmetry and solving problems in geometry and other fields. They are also used in art and design to create interesting visual effects.

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