1. 1
   Triangle ABC has vertices A(1,1), B(4,1) and C(1,3). Triangle ABC is translated by the column vector $\begin{pmatrix}3\\-2\end{pmatrix}$ to form triangle A'B'C'.

   (a)

   What are the coordinates of A'?

   [1 mark]

   • A(-2, -1)
   • B(4, 3)
   • C(4, -1)
   • D(1, 3)

   (b)

   What are the coordinates of B'?

   [1 mark]

   • A(1, -1)
   • B(7, -1)
   • C(7, 3)
   • D(4, -1)

   (c)

   What single transformation maps triangle A'B'C' back onto triangle ABC?

   [1 mark]

   • AEnlargement, scale factor $-1$
   • BReflection in the x-axis
   • CRotation of 180° about the origin
   • DTranslation by $\begin{pmatrix}-3\\2\end{pmatrix}$

   Total for question 1: 3 marks

2. 2
   Point P has coordinates (2, 5) and is reflected in the line $x=1$ to give point P'. Point Q has coordinates (-3, 2) and is reflected in the y-axis to give point Q'.

   (a)

   Find the coordinates of P', the image of P after reflection in the line $x=1$.

   [2 marks]

   (b)

   Find the coordinates of Q', the image of Q after reflection in the y-axis.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Triangle DEF has vertices D(2,1), E(5,1), F(2,4). Triangle DEF is rotated 90° clockwise about the origin to form triangle D'E'F'.

   (a)

   Find the coordinates of D' and E' after this rotation.

   [3 marks]

   (b)

   Find the coordinates of F', and state whether the rotation changes the area of the triangle, giving a reason.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Shape S has vertices at (1,1), (3,1) and (1,4). Shape S is enlarged by scale factor 2, centre (0,0), to form shape T. Shape T is then translated by vector $\begin{pmatrix}-2\\1\end{pmatrix}$ to form shape U.

   (a)

   Find the coordinates of the vertices of shape T.

   [4 marks]

   (b)

   Find the coordinates of the vertices of shape U.

   [4 marks]

   (c)

   Calculate the area of shape S, then use the properties of enlargement and translation to find the area of shape U, explaining your reasoning.

   [5 marks]

   Total for question 4: 13 marks

End of questions