https://file.aiquickdraw.com/mathbot/file/172957169064979gq5so9.jpg

The image shows a diagram where the quadrilateral ABCD is rotated 90° counterclockwise about the origin, denoted as \( r(90^\circ, O)(ABCD) \). The task is to determine the coordinates of points A, B, C, and D after the rotation.

### Step-by-step solution:
When a point \((x, y)\) is rotated by 90° counterclockwise about the origin, the new coordinates become \((-y, x)\).

Let's apply this to the given points from the diagram:

#### 1. Original coordinates:
- Point A: \((4, 2)\)
- Point B: \((3, -1)\)
- Point C: \((0, -2)\)
- Point D: \((1, 3)\)

#### 2. After 90° counterclockwise rotation:
- For Point A \((4, 2)\), the new coordinates are \((-2, 4)\).
- For Point B \((3, -1)\), the new coordinates are \((1, 3)\).
- For Point C \((0, -2)\), the new coordinates are \((2, 0)\).
- For Point D \((1, 3)\), the new coordinates are \((-3, 1)\).

### Final coordinates after the rotation:
- Point A: \((-2, 4)\)
- Point B: \((1, 3)\)
- Point C: \((2, 0)\)
- Point D: \((-3, 1)\)

Would you like further details or have any questions?

#### 5 Related Questions:
1. How would the coordinates change for a 180° rotation around the origin?
2. What is the general formula for a 270° counterclockwise rotation?
3. How do we determine the center of rotation if not given as the origin?
4. Can we use matrices to represent 2D rotations? How?
5. How would a clockwise rotation differ in terms of coordinate transformations?

#### Tip:
When performing 2D rotations, visualizing the change by drawing or tracing a small portion of the graph can help clarify the transformation effect.

The diagram shows r(90°, O)(ABCD). What are the coordinates of ABCD?

Determine the new coordinates of quadrilateral ABCD after a 90° counterclockwise rotation about the origin. The image involves applying the rotation formula and understanding coordinate transformations, suitable for students in Grades 8-10.

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