Back to Define transformations formally — Problem 3 · 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.

$A line of reflection with point P on the line; P maps to itself.$

The formal definition of a reflection across line $\ell$ states that $P$ maps to $P'$ such that $\ell$ is the perpendicular bisector of $PP'$ . For a point $P$ that lies directly on line $\ell$ , where does $P$ map?

P maps to a point on the opposite side of the line at distance 1.

$P$ maps to itself ( $P' = P$ ).

$P$ maps to the foot of the perpendicular from $P$ to $\ell$ .

$P$ maps to the reflection of $\ell$ itself.