To determine which graph shows a rotation of triangle PQR about the origin (0, 0), let's consider how a rotation works. For example, if you rotate a point 90 degrees counterclockwise around the origin, the coordinates (x, y) become (-y, x). Similarly, here are transformations for key rotations:
- 90° Counterclockwise: (x, y) → (-y, x)
- 180°: (x, y) → (-x, -y)
- 270° Counterclockwise: (x, y) → (y, -x)
Examine the vertices of triangle PQR in each graph and compare them with the transformations of original points based on the rotation definition. Unfortunately, without the visual representation of the graphs, I cannot definitively tell which graph corresponds to the correct rotation.
However, based on this understanding, you can compare the coordinates of points P, Q, and R with their corresponding points after applying the appropriate transformation. Identify the graph where the positions of the transformed points match the new points in the rotation you suspect.
If you have specific coordinates for points P, Q, and R, you can do this calculation for yourself to see which graph accurately reflects the rotation about the origin.