Back to Define transformations formally — Problem 5 · 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 rotation by angle $\theta$ about center $O$ states that $P$ maps to $P'$ such that two conditions hold (when $P \neq O$ ). Which pair correctly states both conditions?

$OP = OP'$ , and the straight-line distance from $P$ to $P'$ equals $\theta$ .

$P'$ lies on the perpendicular bisector of $OP$ , and angle $POP' = \theta$ .

$OP = OP'$ (so $P'$ lies on the circle centered at $O$ through $P$ ), and the measure of angle $POP' = \theta$ .

$P'$ lies on the same horizontal line as $P$ , and angle $POP' = \theta$ .