To find the coordinates of the point (1, 2) after a rotation of 180 degrees about the origin, we can use a simple rule for rotation in the Cartesian coordinate system.
A rotation of 180 degrees around the origin inverts the coordinates of the point. This means that the transformation can be expressed mathematically as:
New Coordinates = (-x, -y)
For the point (1, 2), we will apply this transformation:
- Original x-coordinate: 1
- Original y-coordinate: 2
Now, applying the rotation:
- New x-coordinate = -1
- New y-coordinate = -2
Therefore, the coordinates of the point (1, 2) after a 180-degree rotation about the origin will be (-1, -2).
To visualize this, imagine your coordinate plane. Starting at (1, 2), you would move three units to the left (to -1) and two units down (to -2) to land at the new point. This helps confirm that the rotation and transformation you performed are correct. In conclusion, the final coordinates after the rotation are (-1, -2).