Answer:The final point after both transformations would be (-3, -2).
Explanation:
To perform a rotation with center (0,0) of 90 degrees clockwise followed by a reflection in the x-axis, you can follow these steps:
1. **Rotation by 90 degrees clockwise:** This rotation will change the coordinates of a point (x, y) to (-y, x). In other words, the x-coordinate becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.
So, if you have a point (x, y) and you rotate it by 90 degrees clockwise, it becomes (-y, x).
2. **Reflection in the x-axis:** A reflection in the x-axis changes the sign of the y-coordinate while leaving the x-coordinate unchanged.
So, if you have a point (-y, x) and you reflect it in the x-axis, it becomes (-y, -x).
So, if you want to apply a rotation of 90 degrees clockwise followed by a reflection in the x-axis to a point (x, y), the resulting point would be (-y, -x).
For example, if you have a point (2, 3) and you apply these transformations:
1. Rotate 90 degrees clockwise: (-3, 2)
2. Reflect in the x-axis: (-3, -2)
The final point after both transformations would be (-3, -2).