Understand turns or rotations

Today we will learn how to understand turns or rotations. Math helps us solve problems and understand the world around us.

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).

Let's break this down step by step so it's easy to understand. Follow along with the examples, and don't worry if it takes some practice to get the hang of it!

Remember: Making mistakes is part of learning. If something is tricky, try again, look at the examples, or ask for help.