Lesson 4: Compose Transformations

Property

A composition of reflections is a transformation where a figure is reflected across a line, and then its image is reflected across a second line. The notation for a composition is $(R_m \circ R_l)(P) = R_m(R_l(P))$, which means a reflection of point $P$ across line $l$ followed by a reflection across line $m$.

Examples

Property

A sequence of transformations, or a composition, maps a preimage figure $F$ to a final image figure $F''$. This can be represented as $F'' = (T_2 \circ T_1)(F)$, where transformation $T_1$ is applied first, followed by $T_2$. For any given preimage and image, there can be multiple different sequences of transformations that produce the same result.

Examples