Let's break down the transformations one by one to determine the correct description.

Given Transformations:

1. $(x, y) \rightarrow (x - 2, y + 3)$
2. $(x, y) \rightarrow (-x, y)$
3. $(x, y) \rightarrow (x, -y)$
4. $(x, y) \rightarrow (-y, -x)$

Analyzing Each Transformation:

1. $(x, y) \rightarrow (x - 2, y + 3)$:

   • This transformation shifts $x$ by $-2$ and $y$ by $+3$.
   • This is a translation: 2 units to the left and 3 units up.

2. $(x, y) \rightarrow (-x, y)$:

   • This transformation reflects the point over the $y$-axis (because it changes the sign of $x$).
   • This is a reflection over the $y = 0$ mirror line (which is the y-axis).

3. $(x, y) \rightarrow (x, -y)$:

   • This transformation reflects the point over the $x$-axis (because it changes the sign of $y$).
   • This is a reflection over the $x = 0$ mirror line (which is the x-axis).

4. $(x, y) \rightarrow (-y, -x)$:

   • This transformation rotates the point by 90 degrees clockwise and then reflects it over the origin.
   • This is equivalent to a rotation by 90° clockwise around the origin.

Matching with the Options:

Given the breakdown:

• Translation 2 units to the left and 3 units up corresponds with the first transformation.
• Reflection over the $y = 0$ mirror line (y-axis) corresponds with the second transformation.
• Reflection over the $x = 0$ mirror line (x-axis) corresponds with the third transformation.
• A 90° clockwise rotation corresponds with the fourth transformation.

The correct sequence described matches with the description in the fourth option:

• Translation 2 units to the left and 3 units up.
• $R_{90^\circ}$ (90° rotation clockwise).
• Reflection over the $y = 0$ mirror line.
• Reflection over the $x = 0$ mirror line.

Answer: The correct answer is the last option.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What would the sequence look like if the order of transformations was reversed?
2. How would a translation of 3 units down and 2 units right affect the result?
3. What if the rotation was 90° counterclockwise instead of clockwise?
4. How does a reflection over the origin differ from these transformations?
5. What is the net effect of performing a reflection over both axes?

Tip: When analyzing multiple transformations, it helps to go step by step and visualize or sketch the intermediate steps.