Question

Identify a sequence of rigid transformations that would map ABCD→A"B"C"D" . Give your answer in the form of a composition transformation mapping. (1 point) (x,y)→(−x,y−4)
(x,y)→(x,−y−4)
(x,y)→(x,y+4)
(x,y)→(−x−4,y)

Answer 1

To map the quadrilateral ABCD to A"B"C"D" using the provided transformations, we need to identify a sequence of operations that takes the coordinates of ABCD to the coordinates of A"B"C"D".

Let's analyze the given transformations one by one:

1. **(x,y)→(−x,y−4)**: This transformation reflects the point over the y-axis and then translates it down 4 units.
2. **(x,y)→(x,−y−4)**: This transformation keeps the x-coordinate the same and reflects the y-coordinate over the x-axis, then translates it down 4 units.
3. **(x,y)→(x,y+4)**: This transformation translates the point up 4 units.
4. **(x,y)→(−x−4,y)**: This transformation reflects the point over the y-axis and translates it left 4 units.

To find the appropriate sequence to transform ABCD into A"B"C"D", we typically need to understand the specific changes in coordinates of points A, B, C, and D. However, without the specific positions of the points, I'll guide you through a suitable approach.

### Suggested Composition of Transformations:
1. **Start with Translation**: If you need to move the points vertically, start with (x,y)→(x,y+4) to shift up.
2. **Next, Reflect or Translate**: You might need to apply either a reflection or another translation based on the relative positions of ABCD to A"B"C"D".
3. **Final Steps**: You can then apply another transformation if a reflection is necessary.

A possible composition could look like this (in general terms):

1. **First Transformation**: (x,y)→(x,y+4) (Translate up 4 units)
2. **Second Transformation**: (x,y)→(−x,y−4) (Reflect over the y-axis and translate down)

So, the composition would be:

\[
(x,y) \xrightarrow{(x,y)\to(x,y+4)} (x,y+4) \xrightarrow{(x,y)\to(-x,y-4)} (-x,y) \rightarrow (-x,y-4)
\]

If you need exact transformations that lead precisely to A"B"C"D", please provide the specific coordinates of ABCD and A"B"C"D" for a more accurate analysis.