Enlargement by rational scale factorsIB MYP Maths Extended: Subtopic test

1. 1
   Triangle $ABC$ has vertices $A(2,2)$, $B(6,2)$ and $C(6,8)$. It is enlarged with centre the origin $O$ and scale factor $\frac12$ to give triangle $A'B'C'$.

   (a)

   Find the coordinates of $C'$.

   [1 mark]

   • A$(12,16)$
   • B$(3,4)$
   • C$(-3,-4)$
   • D$(6,8)$

   (b)

   Find the area of triangle $A'B'C'$, in square units.

   [1 mark]

   • A$6$
   • B$12$
   • C$3$
   • D$24$

   (c)

   Triangle $A''B''C''$ is the image of $ABC$ under an enlargement with centre $O$ and scale factor $-\frac12$. Find the coordinates of $B''$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Triangle $T$ has vertices $(2,1)$, $(3,1)$ and $(3,3)$. Triangle $T'$ has vertices $(-1,1)$, $(-3,1)$ and $(-3,-3)$. $T'$ is the image of $T$ under a single enlargement.

   (a)

   What is the scale factor of the enlargement?

   [1 mark]

   • A$2$
   • B$\frac12$
   • C$-\frac12$
   • D$-2$

   (b)

   What are the coordinates of the centre of the enlargement?

   [1 mark]

   • A$(1,1)$
   • B$(0,0)$
   • C$(2,1)$
   • D$(-1,-1)$

   (c)

   A different shape of area 5 cm$^2$ is enlarged by the same enlargement (the same centre and scale factor). Find the area of its image.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A sculptor makes a clay model of a statue. The model is an enlargement of the statue with scale factor $\frac{1}{20}$. The statue is 6 m high, has a surface area of 48 m$^2$ and a volume of 21 m$^3$.

   (a)

   Find the height of the model in centimetres and the surface area of the model in cm$^2$.

   [3 marks]

   (b)

   The clay used for the model has density 1.8 g/cm$^3$. Find the mass of the model in kilograms.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A company packs tea in tins that are cubes. The small tin has sides of length 10 cm. Other tins are made as enlargements of the small tin with scale factor $k$. A tin is always completely full of tea.

   (a)

   (i) Find the surface area and the volume of the tin when $k=\frac12$ and when $k=3$.
   (ii) Describe how the surface area and the volume of a tin change when its side length is multiplied by $k$. Write each as a general rule.
   (iii) Use your rule to find the volume of the tin when $k=2.5$.

   [6 marks]

   (b)

   The small tin sells for 6 AED. The large tin, with $k=2$, sells for 40 AED. The tea costs the company 0.003 AED per cm$^3$. The metal for the small tin costs 1.20 AED, and the cost of metal is proportional to surface area. Ignore all other costs.
   Evaluate whether the large tin is a better choice for (i) the customer and (ii) the company. Justify your answer with calculations.

   [6 marks]

   Total for question 4: 12 marks

End of questions