Stage 8 - Q1 - 3 marks
Enlarge P by scale factor 2 about the origin.
Hint
Multiply both coordinates by two because the centre is the origin.
Stage 8 - Q2 - 3 marks
Enlarge P by scale factor 3 about K\((1,1)\).
Hint
Multiply displacement (2,1) by three, then add K.
Stage 8 - Q3 - 4 marks
Enlarge ABC by scale factor 2 about K\((1,1)\).
Hint
Double each displacement from the centre.
Stage 8 - Q4 - 2 marks
A side of length 4 cm becomes 12 cm. What is the positive enlargement scale factor? Would its angles triple?
Hint
Distinguish lengths from angles.
Stage 8 - Q5 - 4 marks
An enlargement of scale factor 3 about \((1,1)\) gives image \((7,10)\). Find the original point.
Hint
Undo the scale on displacements, not on absolute coordinates.
Stage 8 - Q6 - 4 marks
Triangle ABC has A\((2,2)\), B\((4,2)\), C\((2,5)\). It is enlarged by scale factor 3 about A. Which vertex stays fixed, and why?
Hint
Look at the centre’s own displacement.
Stage 8 - Q7 - 4 marks
A rectangle is 3 cm by 5 cm. It is enlarged by scale factor 2. Compare its old and new perimeter and area.
Hint
Calculate both quantities from the changed dimensions.
Stage 8 - Q8 - 4 marks
A point is enlarged by scale factor 2 about K, then by scale factor 3 about the same K. Find the single equivalent scale factor and explain.
Hint
Track displacement from the unchanged centre.
Stage 8 - Q9 - 5 marks
P\((2,1)\) is enlarged by scale factor 2 about \((0,0)\), then by scale factor 2 about \((1,0)\). Find the final image. Explain why simply multiplying the original coordinates by four fails.
Hint
A change of centre changes the coordinate offset.
Stage 8 - Q10 - 6 marks
An enlargement with scale factor 2 maps P\((1,3)\) to P′\((-2,5)\). Find its centre K, then find the image of Q\((5,2)\).
Hint
One corresponding pair determines the centre when the non-unit scale factor is known.