Introduction to transformations | Transformations | Geometry | Khan Academy
Khan Academy・2 minutes read
Transformations in mathematics include translations, rotations, and reflections, each involving different ways of changing the position or orientation of shapes while maintaining specific characteristics like lengths and angles. Rigid transformations like translations, rotations, and reflections preserve shape integrity, while non-rigid transformations such as scaling or distorting shapes do not maintain these properties.
Insights
- Rigid transformations such as translations, rotations, and reflections preserve lengths and angles, ensuring that the shape remains unchanged throughout the transformation process.
- Non-rigid transformations, unlike rigid ones, involve scaling or distorting shapes, altering their integrity and structure rather than maintaining their original form.
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Recent questions
What is a translation in mathematics?
Moving all points in the same direction by the same amount.
How are rotations defined in mathematics?
Rotating points around a specific point while maintaining shape.
What do reflections create in mathematics?
Mirror images of shapes across a line.
What are rigid transformations in mathematics?
Transformations that maintain lengths and angles.
What distinguishes non-rigid transformations from rigid transformations in mathematics?
Non-rigid transformations involve scaling or distorting shapes.
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Summary
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Mathematical Transformations: Translations, Rotations, Reflections, and More
- Transformation in mathematics involves changing mathematical elements like coordinates or points into different ones.
- A translation is a transformation where all points are moved in the same direction by the same amount.
- Rotations involve rotating points around a specific point, maintaining the shape but changing the orientation.
- Reflections create mirror images of shapes across a line of symmetry.
- Rigid transformations, like translations, rotations, and reflections, maintain lengths and angles.
- Non-rigid transformations involve scaling or distorting shapes, unlike rigid transformations that maintain shape integrity.
