Combination of Transformations Flashcards

All 5 cards in this deck

What does it mean to say a point is invariant under a transformation?

The point maps onto itself — it stays in exactly the same position.

What single transformation is equivalent to two reflections in parallel mirror lines?

e.g. reflect in $x=2$, then in $x=6$

A translation perpendicular to the lines, of twice the distance between them.

e.g. translation by vector $\binom{8}{0}$.

What single transformation is equivalent to two reflections in perpendicular mirror lines?

e.g. reflect in the $x$-axis, then in the $y$-axis

A rotation of $180^\circ$ about the point where the two lines cross.

e.g. rotation of $180^\circ$ about $(0,0)$.

True or false? Doing two transformations in the opposite order always gives the same final image.

False. Order usually matters, e.g. reflecting in the $x$-axis then in $y=x$ gives a $90^\circ$ rotation one way, the other order gives the $90^\circ$ rotation the other way.

When asked to describe fully the single transformation equivalent to a combination, how many transformations may your answer contain?

Exactly one — no marks are given if more than one transformation is described.