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Geometry & measures · Transformations

Chapter 1 · 4

The idea

Reflections & rotations

Reflecting in named mirror lines including y = x and y = −x, rotating about a given centre with a sense, and the exact wording needed to DESCRIBE a transformation for full marks.

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Geometry & measures · Transformations

Reflections & rotations

Reflecting in named mirror lines including y = x and y = −x, rotating about a given centre with a sense, and the exact wording needed to DESCRIBE a transformation for full marks.

Why it works

Same shape, same size, new position

A transformation moves every point by the same rule. Reflections and rotations are congruent transformations: the image is the same shape and the same size as the object — only its position or orientation changes. That is the first thing an exam answer can say about them, and the reason tracing paper works at all.

Reflection: across the mirror, same distance

If AA is 3 squares above the mirror line, A′A' is 3 squares below it, measured perpendicular to the line. So reflect one vertex at a time, then join up. In the two diagonal cases the coordinates swap:

in y=x:(a,b)↦(b,a),in y=−x:(a,b)↦(−b,−a).\text{in } y = x: (a, b) \mapsto (b, a), \qquad \text{in } y = -x: (a, b) \mapsto (-b, -a).

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