Question: Triangle R has been rotated clockwise/anticlockwise by ° about the point ( , ) to give triangle S. x marks the centre of rotation Triangle R is a right triangle in the top-right of the graph with vertices at (1,1), (1,4), and (3,1); triangle S is the matching right triangle below the x-axis with vertices at (1,-1), (1,-3), and (4,-1); the red x marking the centre of rotation is at the origin (0,0).

1. **State the problem:** We have triangle R with vertices at $ (1,1), (1,4), (3,1) $ rotated about the origin $ (0,0) $ to form triangle S with vertices at $ (1,-1), (1,-3), (4,-1) $. We need to find the angle and direction of rotation. 2. **Recall rotation rules about the origin:** - A rotation of $90^\circ$ clockwise maps $ (x,y) \to (y,-x) $. - A rotation of $90^\circ$ anticlockwise maps $ (x,y) \to (-y,x) $. - A rotation of $180^\circ$ maps $ (x,y) \to (-x,-y) $. 3. **Check vertex $ (1,1) $ under rotations:** - $90^\circ$ clockwise: $ (1,1) \to (1,-1) $ matches vertex in S. - $90^\circ$ anticlockwise: $ (1,1) \to (-1,1) $ no match. - $180^\circ$: $ (1,1) \to (-1,-1) $ no match. 4. **Check vertex $ (1,4) $ under $90^\circ$ clockwise:** $ (1,4) \to (4,-1) $ matches vertex in S. 5. **Check vertex $ (3,1) $ under $90^\circ$ clockwise:** $ (3,1) \to (1,-3) $ matches vertex in S. 6. **Conclusion:** All vertices match after a $90^\circ$ clockwise rotation about the origin. **Final answer:** Triangle R is rotated $90^\circ$ clockwise about the point $ (0,0) $ to give triangle S.