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.