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The task is to rotate the given figure 270 degrees counterclockwise. To achieve this, we apply the following transformation for a 270° counterclockwise rotation about the origin in the coordinate plane:

- The point \((x, y)\) transforms to \((y, -x)\).

Let’s apply this transformation to each point in the figure:

1. **Point D** is at \((2, -3)\). After the transformation, \(D'\) will be at \((-3, -2)\).
2. **Point E** is at \((2, 0)\). After the transformation, \(E'\) will be at \((0, -2)\).
3. **Point F** is at \((4, 2)\). After the transformation, \(F'\) will be at \((2, -4)\).
4. **Point G** is at \((5, -1)\). After the transformation, \(G'\) will be at \((-1, -5)\).

Now that we have the coordinates of the transformed points, we can compare them to the options provided:

- Option A shows the figure rotated and positioned at these new points: \(D'(-3, -2)\), \(E'(0, -2)\), \(F'(2, -4)\), and \(G'(-1, -5)\), which matches the calculated result.

Thus, **Option A** is the correct answer for a 270-degree counterclockwise rotation.

Would you like any more details or have any questions?

Here are 5 questions to expand on this:

1. What is the transformation rule for a 90-degree clockwise rotation?
2. How do you determine the direction of rotation in geometry?
3. What is the effect of a 180-degree rotation on any point \((x, y)\)?
4. Can you describe the transformation for a reflection across the x-axis?
5. How does a rotation differ from a reflection in terms of point mapping?

**Tip:** When rotating points, always verify the rotation direction and apply the transformation rules consistently for all vertices.

Rotate the following figure 270 degrees counterclockwise.

Learn how to rotate a polygon 270 degrees counterclockwise on the coordinate plane using the transformation formula (x, y) -> (y, -x). This problem covers concepts in coordinate geometry and is suitable for students in grades 8-10.

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