Back to Define transformations formally — Problem 1 · Task Set 4

Exercises: Define Transformations Formally

Work through each section in order. For problems asking you to state or explain definitions, use precise geometric vocabulary — no coordinates unless specifically requested.

Grade 9·20 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-co-a-4

Work through problems with immediate feedback

Fluency Practice

Apply the formal geometric definitions of translation, reflection, and rotation.

The formal definition of a translation along directed segment $\overrightarrow{AB}$ states that each point $P$ maps to $P'$ such that segment $PP'$ satisfies which three conditions?

$PP'$ is parallel to $AB$ ; the length of $PP'$ equals the length of $AB$ ; $PP'$ points in the same direction as $AB$ .

$PP'$ is perpendicular to $AB$ ; the length of $PP'$ equals the length of $AB$ ; $P$ is the midpoint of $AB$ .

The coordinate rule $(x, y) \to (x + a, y + b)$ is applied to $P$ ; the result equals $P'$ .

$PP'$ bisects $AB$ ; the direction from $P$ to $P'$ is counterclockwise; $PP'$ has any length.