Transformations overview

This lesson focuses on transformations overview. Mathematics provides tools for modeling and analyzing complex systems.

Geometric transformations move, flip, turn, or resize figures. Translation (slide): every point moves the same distance in the same direction; shape and size preserved. Reflection (flip): a mirror image over a line of reflection; shape and size preserved; orientation reversed. Rotation (turn): figure turns about a fixed point (center of rotation) by a given angle and direction. Dilations: scale a figure by a scale factor k from a center; if k > 1, figure grows; if 0 < k < 1, figure shrinks; shape preserved, size changes. Isometries (rigid motions: translation, reflection, rotation) preserve size and shape—the image is congruent to the pre-image. Compositions: applying one transformation then another (the order may matter!). Coordinate rules for common transformations: reflection over x-axis: (x, y) → (x, −y); rotation 90° CCW: (x, y) → (−y, x); rotation 180°: (x, y) → (−x, −y).

As you engage with this material, consider both the theoretical foundations and practical applications. Think critically about how this concept builds on prior knowledge and where you might apply it beyond the classroom.

Challenge yourself to go beyond memorization—seek to understand the "why" behind the processes and principles.