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Geometry › Transformations
Transformations
Slide, flip, turn or scale a shape — the four moves that change a figure's place without breaking it.
Transformation playground
Slide, turn, flip or scale — pick a transformation and watch the L move.
(x, y) → (x + 80, y + 0)
80
0
Congruent
Translate, rotate and reflect keep the shape exactly the same size.
The four basic transformations
- Translation — slide. Every point moves the same distance, in the same direction.
- Rotation — turn around a fixed point by some angle.
- Reflection — flip across a mirror line.
- Resizing (dilation) — scale toward or away from a center.
Congruent vs similar
The first three keep the shape congruent — same size and shape. Resize makes it similar — same shape, scaled.
What stays the same?
- Translate, rotate, reflect: side lengths, angles, area — all unchanged.
- Resize: angles unchanged. Side lengths scale by the factor. Area scales by the factor squared.
Composing transformations
You can chain transformations. Two reflections across parallel lines is the same as a translation. Two reflections across intersecting lines is a rotation. The rules build up.