Stage 8 - Q1 - 3 marks
Translate P by \(\binom{-2}{3}\).
Hint
Add the vector entries to the coordinates.
Stage 8 - Q2 - 3 marks
Reflect P in \(y=x\).
Hint
Swap coordinates.
Stage 8 - Q3 - 3 marks
Rotate P 90 degrees anticlockwise about the origin.
Hint
Use (x,y)↦(−y,x).
Stage 8 - Q4 - 3 marks
Enlarge P by scale factor 3 about K\((1,0)\).
Hint
Triple displacement (2,2) and add the centre.
Stage 8 - Q5 - 4 marks
A transformation preserves all lengths but reverses orientation. Which of translation, reflection, rotation and positive enlargement fits this description? Explain.
Hint
Compare the ordering of corresponding vertices.
Stage 8 - Q6 - 4 marks
Reflect \((2,5)\) in the x-axis, then translate by \((3,1)\). Reverse the order and compare the results.
Hint
Do both sequences one step at a time.
Stage 8 - Q7 - 4 marks
A half turn about K maps \((4,2)\) to \((-2,6)\). Find K. Then reflect K in \(y=-x\).
Hint
Solve the centre problem before the second transformation.
Stage 8 - Q8 - 5 marks
A point is enlarged by scale factor 2 about the origin, then translated by \((3,-1)\), giving image \((11,5)\). Find the original point.
Hint
Undo a sequence in the reverse order.
Stage 8 - Q9 - 5 marks
Reflect a general point in \(y=x\), then rotate 90 degrees clockwise about the origin. Identify the equivalent single reflection.
Hint
Use a general ordered pair so your conclusion applies to every point.
Stage 8 - Q10 - 6 marks
A triangle has A\((1,1)\), B\((3,1)\) and C\((1,2)\). First enlarge it by factor 2 about K\((1,1)\), then rotate 90 degrees anticlockwise about the same K. Find every final vertex and show that doing the two operations in the opposite order gives the same result.
Hint
The shared centre lets you compare operations on the same displacement vectors.