Point A has a coordinate A(3,2). The point is rotated 180 degrees clockwise about the origin. What is the x-coordinate of the point A’?

To find the coordinates of point \( A' \) after rotating point \( A(3, 2) \) 180 degrees clockwise about the origin, we need to follow these steps:

1. **Understand the transformation**: A 180-degree rotation about the origin will flip the point to the opposite side of the origin. Mathematically, this means changing the sign of both the x and y coordinates of the point.

2. **Apply the transformation**: For a point \( (x, y) \) rotated 180 degrees, the new coordinates \( (x', y') \) are given by:
   \[
   (x', y') = (-x, -y)
   \]

3. **Calculate the new coordinates**: Substitute \( x = 3 \) and \( y = 2 \):
   \[
   x' = -3
   \]
   \[
   y' = -2
   \]

Therefore, the coordinates of point \( A' \) after the rotation are \( (-3, -2) \). The x-coordinate of point \( A' \) is \( -3 \).

If you have any further questions or need additional details, please let me know.

Here are some more questions you might find useful:
1. How do I find the distance between two points in a coordinate plane?
2. What are the properties of rotations in geometry?
3. How do I reflect a point across a given line?
4. What is the equation of a circle given its center and radius?
5. How do I determine the midpoint of a line segment?

Tip: For rotations, reflections, and other transformations in geometry, drawing a diagram can significantly aid in visualizing the problem and understanding the solution process.

Learn how to rotate point A(3, 2) 180 degrees clockwise about the origin and find the x-coordinate of point A'. This problem involves coordinate geometry and transformation concepts. Suitable for students in Grades 7-9.

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