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The problem asks for the coordinates of point \( D' \) after the point \( D(-4, -2) \) is rotated 180° counterclockwise around the origin.

To find the coordinates of a point after a 180° rotation around the origin, we apply the following transformation rule:
\[
(x, y) \rightarrow (-x, -y)
\]

Given \( D(-4, -2) \), the coordinates of the new point \( D' \) are:
\[
D' = (-(-4), -(-2)) = (4, 2)
\]

Thus, the coordinates of \( D' \) are \( (4, 2) \).

Would you like more details or explanations on this? 

Here are five related questions for practice:
1. What are the coordinates of a point \( A(3, -5) \) after a 180° rotation about the origin?
2. How would the point \( B(7, 2) \) look after a 90° clockwise rotation?
3. What happens to a point's coordinates after a 270° counterclockwise rotation?
4. How does a reflection over the origin affect the coordinates of a point?
5. Can you describe the transformation rule for a 180° rotation in general terms?

**Tip:** For any rotation by 180°, the signs of both the \( x \)- and \( y \)-coordinates are reversed.

The point D(-4, -2) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, D'?

Learn how to find the new coordinates of point D(-4, -2) after a 180° counterclockwise rotation around the origin. This problem covers key concepts in coordinate geometry and transformations, suitable for students in Grades 7-9.

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