To find a sequence of rigid transformations that maps rectangle ABCD to rectangle A"B"C"D", we first need to identify what transformations are required. Rigid transformations include translations and reflections.
- If rectangle A B C D is reflected over the y-axis, the mapping can be expressed as
. - Next, if we need to move the new rectangle (after reflection) down by 4 units, this can be expressed as
.
The complete transformation sequence that maps ABCD to A"B"C"D" can be expressed as a composition of these transformations:
- Reflect over the y-axis:
- Translate down by 4 units:
In terms of composition, this can be written as:
- First reflect:
- Then translate:
Putting these operations together, the sequence of transformations is:
However, in terms of a single transformation:
The composition can be represented as:
Therefore, the answer is:
So the final answer is: (x,y)→(−x,y−4).