Stage 8 - Q1 - 3 marks
Rotate P 90 degrees clockwise about the origin.
Hint
A clockwise quarter turn sends (x,y) to (y,−x).
Stage 8 - Q2 - 3 marks
Rotate P 180 degrees about the origin.
Hint
Negate both coordinates.
Stage 8 - Q3 - 4 marks
Rotate triangle ABC 90 degrees anticlockwise about the origin.
Hint
Use (x,y)↦(−y,x) for every vertex.
Stage 8 - Q4 - 2 marks
A 90-degree clockwise rotation about the origin gives image \((-3,6)\). Find the original point.
Hint
Use the opposite direction to reverse a quarter turn.
Stage 8 - Q5 - 4 marks
Compare a 90-degree clockwise rotation and a 270-degree anticlockwise rotation about the origin. Use \((2,5)\) as a check.
Hint
Compare their net angle within a full turn.
Stage 8 - Q6 - 4 marks
Which point stays fixed under a 90-degree rotation about the origin? Explain why no other point can stay fixed.
Hint
Set the image coordinates equal to the original coordinates.
Stage 8 - Q7 - 4 marks
P\((3,-4)\) is rotated 90 degrees anticlockwise twice about the origin. Find its final image and one equivalent rotation.
Hint
Add the two rotation angles.
Stage 8 - Q8 - 4 marks
A point \((6,1)\) undergoes seven successive 90-degree clockwise rotations about the origin. Find its final image without drawing all seven.
Hint
Remove complete groups of four quarter turns.
Stage 8 - Q9 - 5 marks
A 90-degree clockwise rotation maps \((a,3)\) to \((3,2a-6)\). Find a and check the point-image pair.
Hint
Use the coordinate rule to create one equation.
Stage 8 - Q10 - 6 marks
A point P is rotated 90 degrees anticlockwise about the origin to Q. The midpoint of PQ is \((1,4)\). Find P and Q.
Hint
Use the known rotation to express both points using only x and y.