Stage 8 - Q1 - 2 marks
An object side is 3 cm and its image side is 9 cm. Find the scale factor.
Hint
Image length divided by object length.
Stage 8 - Q2 - 2 marks
An enlargement of scale factor 4 gives an image side of 28 cm. Find the original side.
Hint
Undo multiplication by four.
Stage 8 - Q3 - 2 marks
An enlargement has centre \((0,0)\) and maps \((2,3)\) to \((6,9)\). Give its full description.
Hint
Include both centre and scale factor.
Stage 8 - Q4 - 2 marks
Scale factor 2 maps \((3,1)\) to \((5,1)\). Find the centre.
Hint
The image is twice as far from K as the original.
Stage 8 - Q5 - 4 marks
An object has sides 2, 3 and 4 cm. A proposed image has corresponding sides 6, 9 and 11 cm. Can it be an enlargement? Explain.
Hint
Check more than one pair of corresponding lengths.
Stage 8 - Q6 - 4 marks
An enlargement of scale factor 3 maps \((2,1)\) to \((6,1)\). Find its centre and verify that centre stays fixed.
Hint
Solve for the same centre in both coordinate directions.
Stage 8 - Q7 - 4 marks
Two equal-shaped triangles have scale factor 2. A pupil draws rays through non-corresponding vertices and gets two different candidate centres. Explain how to repair the method.
Hint
A ray must join a vertex to its own image.
Stage 8 - Q8 - 5 marks
A positive whole-number enlargement maps A\((1,2)\) to A′\((3,4)\) and B\((3,2)\) to B′\((7,4)\). Find the scale factor and centre.
Hint
Find scale factor from a length before finding the centre.
Stage 8 - Q9 - 5 marks
An enlargement of scale factor 3 fixes P\((2,-1)\). Explain why P must be the centre, then find the image of Q\((4,2)\).
Hint
Set the original point equal to its image in the enlargement equation.
Stage 8 - Q10 - 6 marks
An unknown positive whole-number enlargement maps A\((1,1)\) to A′\((5,3)\) and B\((3,1)\) to B′\((11,3)\). Find the scale factor and centre, then the image of C\((2,4)\).
Hint
Do not try to infer the centre from absolute coordinates before finding the scale factor.