https://file.aiquickdraw.com/mathbot/file/1728504386203kbtn7k6s.jpg

The problem in your image asks for the coordinates of points \( H \), \( I \), \( J \), and \( G \) after a 180° rotation about the origin. The initial coordinates of the points on the graph need to be rotated using the rule for a 180° rotation, which is:

\[
(x, y) \rightarrow (-x, -y)
\]

Let’s apply this transformation to the points on the graph:

1. **Point H**:
   - Initial coordinates are \( H(3, -2) \)
   - After rotation: \( H'(-3, 2) \)

2. **Point I**:
   - Initial coordinates are \( I(1, -4) \)
   - After rotation: \( I'(-1, 4) \)

3. **Point J**:
   - Initial coordinates are \( J(4, -1) \)
   - After rotation: \( J'(-4, 1) \)

4. **Point G**:
   - Initial coordinates are \( G(2, -3) \)
   - After rotation: \( G'(-2, 3) \)

Now, let’s match these results with the answer choices given in the image:

- Option B looks correct: \( G(-2, 3), H(-3, 2), I(-1, 4), J(-4, 1) \).

So the correct answer is **B**.

Would you like more details or have any questions? Here are five questions to deepen your understanding:

1. How does a 90° rotation affect the coordinates of a point?
2. What is the rule for a 270° rotation around the origin?
3. What happens to the orientation of a shape when it undergoes a 180° rotation?
4. How can you use matrix multiplication to perform a rotation?
5. Can you generalize the rotation rule for any angle of rotation?

**Tip:** For rotations in a coordinate plane, remember that each rotation has a specific rule, so knowing these transformations makes it easier to solve such problems quickly.

Rotation 180° about the origin. Find the new coordinates for points H, I, J, and G after the rotation.

Learn how to rotate points H, I, J, and G by 180° about the origin on a coordinate plane. This problem covers geometric transformations and the rule for 180° rotation. Suitable for students in Grades 8-10.

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