Stage 9 - Q1 - 4 marks
Rotate ABC 90° anticlockwise about \((0,0)\), then translate \((2,2)\).
Hint
Translate the displacement from the rotation centre, turn it, then add the centre.
Stage 9 - Q2 - 4 marks
Reflect ABC in \(y=x\), then rotate 180° about \((-1,0)\).
Hint
Translate the displacement from the rotation centre, turn it, then add the centre.
Stage 9 - Q3 - 4 marks
ABC rotates 90° anticlockwise then 180°, both about \((0,-1)\). Give the equivalent single rotation and image.
Hint
Keep the same centre when combining the angles.
Stage 9 - Q4 - 3 marks
ABC is translated by \((2,1)\) then rotated 90° clockwise about \((0,-1)\). Describe how to undo both operations.
Hint
Undo the transformations in reverse order.
Stage 9 - Q5 - 4 marks
For \(P=(-3,1)\), compare a 90° anticlockwise rotation about \((-1,-1)\) then translation \((1,1)\) with the reverse order.
Hint
Write the intermediate coordinate in each order.
Stage 9 - Q6 - 4 marks
Rotate ABC 90° anticlockwise about \((1,1)\), then translate \((3,3)\).
Hint
Translate the displacement from the rotation centre, turn it, then add the centre.
Stage 9 - Q7 - 4 marks
Reflect ABC in \(y=x\), then rotate 180° about \((0,1)\).
Hint
Translate the displacement from the rotation centre, turn it, then add the centre.
Stage 9 - Q8 - 4 marks
ABC rotates 90° anticlockwise then 180°, both about \((-1,1)\). Give the equivalent single rotation and image.
Hint
Keep the same centre when combining the angles.
Stage 9 - Q9 - 4 marks
For \(P=(0,-2)\), compare a 90° anticlockwise rotation about \((1,0)\) then translation \((3,2)\) with the reverse order.
Hint
Write the intermediate coordinate in each order.
Stage 9 - Q10 - 6 marks
A half-turn about \(C=(1,-2)\) is followed by a half-turn about \(D=(4,1)\). Find one equivalent transformation and explain what happens if the order is reversed.
Hint
A half-turn about C maps P to \(2C-P\).