The image of the point (1, -2) after a rotation of 180° about the origin is

To find the image of a point after a rotation, you need to follow these steps:

1. Determine the location of the point (1, -2) in a coordinate plane.
- In this case, the point (1, -2) is located 1 unit to the right of the origin (x-axis) and 2 units below the origin (y-axis).

2. Apply the rotation of 180° to the point.
- A rotation of 180° means the point will move exactly halfway around a circle with the origin as the center.
- The result of a 180° rotation is that the coordinates of the point will become negative.

3. Calculate the new coordinates of the point after the rotation.
- Since the point (1, -2) is to the right of the origin (x-axis), after a 180° rotation, it will be reflected to the left of the origin, resulting in a new x-coordinate of -1.
- Similarly, since the point is below the origin (y-axis), it will be reflected above the origin, resulting in a new y-coordinate of 2.

Therefore, the image of the point (1, -2) after a rotation of 180° about the origin is (-1, 2).