1. 1
   Triangle $ABC$ has vertices $A(1, 2)$, $B(4, 2)$ and $C(4, 6)$.

   (a)

   Triangle $ABC$ is translated by the vector $\begin{pmatrix} -2 \\ 3 \end{pmatrix}$ to form triangle $A'B'C'$. What are the coordinates of $A'$?

   [1 mark]

   • A$(-1, 5)$
   • B$(3, -1)$
   • C$(-1, -1)$
   • D$(3, 5)$

   (b)

   Triangle $ABC$ is reflected in the line $y = 2$ to form triangle $A''B''C''$. What are the coordinates of $C''$?

   [1 mark]

   • A$(4, 10)$
   • B$(4, -2)$
   • C$(-4, -2)$
   • D$(4, 2)$

   (c)

   Triangle $ABC$ is rotated $90°$ clockwise about the origin to form triangle $A'''B'''C'''$. What are the coordinates of $B'''$?

   [1 mark]

   • A$(-2, 4)$
   • B$(2, 4)$
   • C$(-4, 2)$
   • D$(2, -4)$

   Total for question 1: 3 marks

2. 2
   Shape $P$ has vertices $(2, 1)$, $(6, 1)$, $(6, 3)$ and $(2, 3)$. Shape $Q$ is an enlargement of shape $P$ with scale factor $3$ and centre of enlargement $(0, 0)$.

   (a)

   Find the coordinates of the vertices of shape $Q$ that correspond to $(2, 1)$ and $(6, 3)$ on shape $P$.

   [2 marks]

   (b)

   Shape $P$ has an area of $8$ square units. Find the area of shape $Q$, and state whether shape $Q$ is congruent or similar to shape $P$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Shape $R$ has vertices $A(1, 1)$, $B(5, 1)$ and $C(5, 4)$. Shape $S$ is the image of shape $R$ under an enlargement with scale factor $-2$ and centre $(1, 1)$.

   (a)

   Find the coordinates of the vertices $A'$, $B'$ and $C'$ of shape $S$.

   [3 marks]

   (b)

   Explain how a negative scale factor affects the position of the image compared with a positive scale factor of the same magnitude, and calculate the ratio of the area of shape $S$ to the area of shape $R$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Triangle $J$ has vertices $(1, 1)$, $(1, 3)$ and $(3, 1)$.

   (a)

   Triangle $K$ has vertices $(-1, -1)$, $(-1, -3)$ and $(-3, -1)$. Describe fully the single transformation that maps triangle $J$ onto triangle $K$.

   [4 marks]

   (b)

   Triangle $L$ has vertices $(2, -1)$, $(2, 1)$ and $(4, -1)$. Describe fully the single transformation that maps triangle $J$ onto triangle $L$.

   [4 marks]

   (c)

   Triangle $N$ is formed by first reflecting triangle $J$ in the line $x = 0$ (the $y$-axis), then reflecting the image in the line $x = 4$. Find the coordinates of the vertices of triangle $N$, and describe the single transformation that maps triangle $J$ directly onto triangle $N$.

   [5 marks]

   Total for question 4: 13 marks

End of questions