Rotations, reflections and combined transformations.
Example 1
Rotate (7,7) anticlockwise by 90∘ about the origin.
Turn the reference directions anticlockwise, then apply the same change to P.Show worked answer
Answer: (−7,7)
- The rotation matrix has rows (0,−1) and (1,0).
- It sends (x,y) to (−y,x), giving (−7,7).
Example 2
Reflect (10,5) in the x−axis, then rotate anticlockwise by 90∘ about the origin.
Reflect the reference directions in the x-axis, then turn them anticlockwise. Use that order to transform P.Show worked answer
Answer: (5,10)
- The reflection gives (10,−5).
- The rotation sends (x,y) to (−y,x), so the result is (5,10).
Example 3
Rotate (2,2) anticlockwise by 90∘ about the origin.
Turn the reference directions anticlockwise, then apply the same change to P.Show worked answer
Answer: (−2,2)
- The rotation matrix has rows (0,−1) and (1,0).
- It sends (x,y) to (−y,x), giving (−2,2).