Identify the domain of an image that has been **rotated 270 degrees counter-clockwise** about the origin, given the range is (3, -4), (1, -1), (6, -7). 

pick one:

(4, -3), (1, -1), (7, -6)

(4, 3), (1, 1), (7, 6)

(-4, 3), (-1, 1), (-7, 6)

(-3, -4), (-1, -1), (-6, -7)

To determine the domain of an image that has been rotated 270 degrees counterclockwise about the origin, we need to apply the transformation rule for a 270-degree counterclockwise rotation.

When a point \((x, y)\) is rotated 270 degrees counterclockwise, its new coordinates become \((y, -x)\).

Given the range points:
- \((3, -4)\)
- \((1, -1)\)
- \((6, -7)\)

Let's apply the rotation rule to each point:

1. \((3, -4)\) becomes \((-4, -3)\)
2. \((1, -1)\) becomes \((-1, -1)\)
3. \((6, -7)\) becomes \((-7, -6)\)

Thus, the correct domain after the rotation is:

**(-4, -3), (-1, -1), (-7, -6)**

However, this is not listed as an option. Since rotations involve correct correspondence but the provided options seem mismatched, **none** of the provided answers directly match. Please let me know if this was intended for a rotation, or if the range points have changed.

Do you want further explanations or have any other questions?

Here are 5 additional questions related to rotations:
1. How does a 180-degree rotation affect the coordinates of a point?
2. What is the effect of a 90-degree clockwise rotation about the origin on a point \((x, y)\)?
3. How do you determine the new coordinates after a point is rotated 360 degrees?
4. What is the general transformation rule for a 270-degree clockwise rotation?
5. How do you find the image of a point after reflecting it and then rotating it 180 degrees about the origin?

**Tip:** When rotating a point 270 degrees counterclockwise, the x-coordinate and y-coordinate swap, and the new x-coordinate takes the negative sign of the original y-coordinate.

Explore how to determine the domain of an image after rotating it 270 degrees counter-clockwise about the origin. This problem involves applying transformation rules in coordinate geometry and understanding rotational symmetry. Suitable for students in Grades 9-12.

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