Transformation geometry is a mathematical and pedagogic approach to the study of geometry that focuses on groups of geometric transformations and properties that are invariant under them. In other words, it is a way of studying geometry by looking at how shapes can be transformed, or changed, while still maintaining certain properties. Transformations in geometry involve changing a shapes position or orientation. There are five main types of transformations in math: dilation, reflection, rotation, translation, and resizing. Here is a brief explanation of each type:

• Dilation: The image is a larger or smaller version of the preimage; "shrinking" or "enlarging."
• Reflection: The image is a mirrored preimage; "a flip."
• Rotation: The image is a rotated preimage; "a turn."
• Translation: The image is a translated preimage; "a slide."
• Resizing: The shape becomes bigger or smaller.

Transformations can be combined, and a shape can be reflected, rotated, translated, or dilated, or can have a combination of these transformations. Transformations in math are expressed algebraically in the graph functions.