We start with the big idea: a transformation is a rule that changes a shape’s position or size by moving its points. Then we separate rigid transformations from resizing, which is one of the most testable distinctions in the topic.

This chapter breaks down translation and rotation, the two transformations most often tested with coordinates and matrices. Marcus explains how translation is just adding vectors, while rotation turns a point around a center by a fixed angle.

Reflection preserves size and shape but changes orientation, which is why it is a rigid transformation with a twist. This chapter focuses on handedness, common misconceptions, and how mirrors show up in exam questions.

Now the focus shifts to dilation, where a shape expands or contracts while keeping its angles. Marcus explains the scale factor, the rule S(x, y) = (sx, sy), and the key fact that area changes by the square of the scale factor.