Answer:
Step-by-step explanation:The figure FGH is rotated using the origin as the center of rotation, resulting in the image with vertices located at F’(3, –1), G’(2, 1), and H’(1, –2).
To determine which rotation could have taken place, we can analyze the changes in the x-coordinates and y-coordinates of the vertices.
For the x-coordinates:
- The x-coordinate of F has changed from 1 to 3.
- The x-coordinate of G has changed from -1 to 2.
- The x-coordinate of H has changed from 2 to 1.
For the y-coordinates:
- The y-coordinate of F has changed from 3 to -1.
- The y-coordinate of G has changed from 2 to 1.
- The y-coordinate of H has changed from 1 to -2.
From these changes, we can see that:
- The x-coordinates have shifted by 2 units to the right (increased by 2).
- The y-coordinates have shifted by 4 units downwards (decreased by 4).
Therefore, the rotation that could have taken place is a rotation of 90 degrees counterclockwise.
In a 90 degrees counterclockwise rotation, the x-coordinate becomes the negative value of the original y-coordinate, and the y-coordinate becomes the positive value of the original x-coordinate. This matches the changes we observed in the coordinates of the figure FGH and its image.
It is important to note that a clockwise rotation of 270 degrees would also result in the same changes in the coordinates, but a 90 degrees counterclockwise rotation is the most common interpretation in this context.