Quadrilateral 
\[A'B'C'D'\] is the image of quadrilateral 
\[ABCD\] under a rotation about the origin, 
\[(0,0)\].

\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[\small{\llap{-}6}\]
\[\small{\llap{-}7}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[\small{\llap{-}6}\]
\[\small{\llap{-}7}\]
\[y\]
\[x\]
\[B\]
\[C\]
\[D\]
\[\blueD A\]
\[C'\]
\[D'\]
\[\maroonD{A'}\]
\[\maroonD{B'}\]
Determine the angle of rotation.
Choose 1 answer:
Choose 1 answer:
(Choice A)   
\[-90^\circ\]
A
\[-90^\circ\]
(Choice B)   
\[-30^\circ\]
B
\[-30^\circ\]
(Choice C)   
\[30^\circ\]
C
\[30^\circ\]
(Choice D)   
\[90^\circ\]
D
\[90^\circ\]

To determine the angle of rotation for the quadrilateral \(A'B'C'D'\), which is the image of quadrilateral \(ABCD\) under a rotation about the origin \((0, 0)\), we can use the following process:

### Steps:
1. **Analyze the coordinates**: 
   We need to identify whether any of the original points \(A, B, C, D\) and their corresponding image points \(A', B', C', D'\) are given or can be estimated from the grid. However, if they are not directly provided, we can reason based on the standard properties of rotations.

2. **Rotation properties**:
   - A **90° rotation** counterclockwise (positive direction) swaps the coordinates of a point and changes the sign of the new \(x\)-coordinate. Thus, \((x, y) \to (-y, x)\).
   - A **-90° rotation** (clockwise) also swaps the coordinates, but changes the sign of the new \(y\)-coordinate: \((x, y) \to (y, -x)\).
   - A **30° or -30° rotation** is more complex and involves trigonometric transformations, which are less likely for a grid-based problem unless detailed coordinates are given.

3. **Matching the rotation type**:
   Without specific coordinates, the problem typically suggests a grid-based rotation, meaning the answer is likely to involve a common rotation angle such as \(90^\circ\) or \(-90^\circ\). 

### Conclusion:
Given the options and the typical behavior of common rotations, the answer is likely **Choice A**: \(-90^\circ\), which corresponds to a clockwise rotation.

Would you like further clarification or details on the rotation process?

Here are some follow-up questions:
1. How does a positive vs. negative rotation affect the direction of rotation?
2. What are the properties of a 180° rotation?
3. How can trigonometric functions describe general rotations in the plane?
4. What happens to the orientation of a figure after a 90° rotation?
5. How can you determine the center of rotation if it's not the origin?

**Tip:** Always check whether rotation preserves distances and angles, since those are key properties of rigid transformations like rotations.

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin (0, 0). Determine the angle of rotation.
Choose 1 answer:
(Choice A) -90°
(Choice B) -30°
(Choice C) 30°
(Choice D) 90°

This problem explores the rotation of quadrilateral ABCD about the origin and asks students to determine the angle of rotation based on key properties of rotations. Suitable for students in Grades 8-10, it covers the formulas and concepts of coordinate geometry and rigid transformations.

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