One way of thinking about a transformation is to consider what happens to every point on the plane under that transformation. For example, under translation, every (pre-image) point on the plane moves to another (image) point; and no two distinct pre-image points move to the same image point. Under reflection, every point goes to a distinct image-point except for points on the mirror line of symmetry (which stay fixed). In addition, a transformation defines how points move on the plane, and conversely, any statement of how points move on the plane defines some sort of transformation.
Example: In the dynamic sketch below, consider AB and its midpoint C. What happens when you drag (only) point A?
(Points A and C are traced so you can compare A to C, the position of which depends on A.)
Question: How could you describe C as a transformation of A?
Click on the 'Show Answer' button in the dynamic sketch below to check your answer.
Mystery Transformation
Explore More: Click on the 'Link to More Mystery Transform' button above to navigate to another activity on this 'mystery' transformation.
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By Michael de Villiers. Created, 24 July 2013; updated 24 June 2022.