Definition: A transformation is a rule that moves or resizes a figure on the plane, such as a translation, reflection, rotation, or dilation.
What is a transformation?
It changes the position, orientation, or size of a figure. The original is the preimage and the result is the image, with matching points labeled A and A’.
What are the four types?
- Translation: slides every point the same distance in the same direction.
- Reflection: flips over a line.
- Rotation: turns around a point by an angle.
- Dilation: enlarges or shrinks by a scale factor.
The first three are rigid motions: size and shape stay the same. A dilation keeps the shape but not the size.
How do the coordinates change?
Translate the point (3, -2) by 4 right and 5 up: it moves to (7, 3). Reflect (3, -2) over the x-axis: (3, 2).
How do you describe a sequence?
List the steps in order. Order can matter: reflecting then translating may not give the same image as translating then reflecting.
What is a common mistake?
Thinking reflections change the size. They do not, only the orientation.
Example: Moving triangle ABC 6 units left is a translation.