https://file.aiquickdraw.com/mathbot/file/17267820679939qolc440.jpg

H is at (3,3) I is at (4,3) J is at (4,1) K is at (3,1)

To rotate the figure \( HIJK \) 180° around the origin, we use the rule for a 180° rotation. When a point \((x, y)\) is rotated 180° around the origin, its new coordinates become \((-x, -y)\).

The original coordinates of points \( H \), \( I \), \( J \), and \( K \) are:
- \( H(3, 3) \)
- \( I(4, 3) \)
- \( J(4, 1) \)
- \( K(3, 1) \)

Now, applying the 180° rotation transformation to each point:
- \( H(3, 3) \) becomes \( H'(-3, -3) \)
- \( I(4, 3) \) becomes \( I'(-4, -3) \)
- \( J(4, 1) \) becomes \( J'(-4, -1) \)
- \( K(3, 1) \) becomes \( K'(-3, -1) \)

Thus, the rotated figure \( H'I'J'K' \) will have the following coordinates:
- \( H'(-3, -3) \)
- \( I'(-4, -3) \)
- \( J'(-4, -1) \)
- \( K'(-3, -1) \)

If you'd like a further explanation or a graph showing the rotation, feel free to ask!

Here are 5 related questions:
1. What is the rule for rotating a figure 90° counterclockwise around the origin?
2. How would a 270° clockwise rotation affect the coordinates of the figure?
3. Can the rotation rule change if the center of rotation is not the origin?
4. How do you find the distance between two points before and after rotation?
5. What is the impact of reflecting the figure across the y-axis instead of rotating it?

**Tip**: To ensure the accuracy of your rotations, always double-check the transformation rule you're using and whether it's clockwise or counterclockwise.

Rotate figure HIJK 180° around the origin. The points are H(3, 3), I(4, 3), J(4, 1), and K(3, 1).

Learn how to rotate the quadrilateral HIJK by 180° around the origin. The original points are H(3, 3), I(4, 3), J(4, 1), and K(3, 1), and the rotated points become H'(-3, -3), I'(-4, -3), J'(-4, -1), and K'(-3, -1). This example illustrates the transformation rule for rotating figures on the coordinate plane, suitable for Grades 7-9.

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