transformation and similarity unit
A transformation is a mathematical operation that changes the position, size, or shape of a figure. It can include translations, rotations, reflections, and dilations.
- Translation: A translation is a transformation that slides an object from one location to another without changing its shape or orientation. It involves moving every point of the object in the same direction by the same distance.
- Rotation: A rotation is a transformation that turns an object around a fixed point called the center of rotation. The object is turned by a certain angle in a clockwise or counterclockwise direction.
- Reflection: A reflection is a transformation that flips an object over a line called the line of reflection. Each point on the object is mapped to a corresponding point on the other side of the line, maintaining the same distance but changing the orientation.
- Dilation: A dilation is a transformation that changes the size of an object. It involves stretching or shrinking the object by a certain scale factor relative to a fixed center point.
Similarity refers to the property of figures having the same shape but not necessarily the same size. Similarity transformations preserve the shape of the figure while changing its size. The most common similarity transformation is a dilation, but it can also include reflections and rotations.
In the unit on transformation and similarity, students typically learn how to identify and perform various transformations, determine the image of a figure after a given transformation, and explore the properties of similar figures. They also learn about the concept of scale factor and how it relates to dilations and similarity.