https://file.aiquickdraw.com/mathbot/file/1726581290177y76kauc8.jpg

The problem asks for the coordinates of the point \( H' \) after rotating point \( H \) by 180° about the origin.

### Step-by-step Solution:
1. **Identify the coordinates of point \( H \)**:
   From the image, we can see that the original coordinates of point \( H \) are approximately \( (-2, 3) \).

2. **Apply the rule for 180° rotation**:
   When a point \( (x, y) \) is rotated by 180° about the origin, the new coordinates \( (x', y') \) are given by:
   \[
   (x', y') = (-x, -y)
   \]
   This means both the x- and y-coordinates change their signs.

3. **Calculate the coordinates of \( H' \)**:
   Using the formula, the coordinates of \( H \) are \( (-2, 3) \). After rotation:
   \[
   H' = (-(-2), -(3)) = (2, -3)
   \]

Thus, the coordinates of \( H' \) after the rotation will be \( (2, -3) \).

### Correct Answer:
The correct option is **(2, -3)**.

Would you like any further explanation or more details?

Here are some related questions:
1. What are the general rules for rotating points by 90°, 180°, and 270° about the origin?
2. How would the coordinates change if we applied a reflection instead of rotation?
3. Can you find the new coordinates after a 90° clockwise rotation?
4. How does a 360° rotation affect the coordinates of a point?
5. What transformations leave a point at its original position?

**Tip**: When rotating points, always remember that a 180° rotation flips both the x- and y-coordinates in sign.

After the rotation, what will be the coordinates of H'?

Determine the new coordinates of a point after rotating it by 180 degrees about the origin. Learn how to apply the 180-degree rotation rule, which flips the signs of both the x- and y-coordinates. Suitable for students in Grades 7-9.

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