The two transformations you've provided appear to describe different types of reflections or rotations of points in the coordinate plane. Let’s break down what each one represents:

1. Transformation C: (x, y) → (–x, –y)

• Description: This transformation reflects a point across the origin (0,0).
• Effect: For any point $(x, y)$, after applying this transformation, the new coordinates will be $(-x, -y)$. This means the point is mirrored in both the x-axis and the y-axis.
• Geometric Meaning: The point $(x, y)$ is reflected through the origin. If you think of the point's position as being in one quadrant, its reflection will be in the opposite quadrant.

Example:

• Original point: $(2, 3)$
• Transformed point: $(-2, -3)$

2. Transformation D: (x, y) → (–y, –x)

• Description: This transformation swaps the coordinates and changes the signs.
• Effect: For any point $(x, y)$, after applying this transformation, the new coordinates will be $(-y, -x)$. It’s like a rotation of 90° counterclockwise (or 270° clockwise) followed by reflection through the origin.
• Geometric Meaning: The transformation swaps the x- and y-values and reflects them both. This results in a 90° counterclockwise rotation of the point.

Example:

• Original point: $(2, 3)$
• Transformed point: $(-3, -2)$

---

In Summary:

• Transformation C: Reflects the point through the origin, changing both x and y signs.
• Transformation D: Swaps the coordinates and changes the signs of both.

Would you like further details or examples? Let me know if you have any questions!

---

Related Questions:

1. How does the reflection across the x-axis differ from the origin reflection?
2. What is the effect of rotating a point by 90° counterclockwise on the coordinate plane?
3. How can you describe a 180° rotation in terms of transformations on the plane?
4. How do these transformations affect the distance of the point from the origin?
5. How do transformations like C and D impact symmetry in geometric figures?

Tip: To understand the transformations visually, try plotting a few points on graph paper and apply the transformations. It will give you a clearer sense of how each one works!