1. 1
   Triangle ABC has vertices A(1, 2), B(3, 2) and C(3, 5), given as coordinates on a grid (no diagram provided).

   (a)

   Find the coordinates of the image of A after a reflection in the x-axis.

   [1 mark]

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

   (b)

   Find the coordinates of the image of B after a rotation of 90 degrees clockwise about the origin.

   [1 mark]

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

   (c)

   Find the coordinates of the image of C after a translation by the column vector $\binom{-2}{4}$.

   [1 mark]

   • A(5, 1)
   • B(1, 9)
   • C(1, 1)
   • D(5, 9)

   Total for question 1: 3 marks

2. 2
   Point D(4, -1) and point E(-2, 3) are both enlarged with centre the origin O and scale factor 3.

   (a)

   Find the coordinates of the image of D.

   [2 marks]

   (b)

   Find the coordinates of the image of E.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Triangle PQR has vertices P(2, 1), Q(2, 4) and R(5, 1). It is first reflected in the y-axis, then translated by the vector $\binom{3}{-2}$.

   (a)

   Find the coordinates of the image of P after both transformations.

   [3 marks]

   (b)

   Find the coordinates of the image of R after both transformations.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Triangle XYZ has vertices X(1, 1), Y(4, 1) and Z(1, 3). Triangle X'Y'Z' is the image of XYZ under a rotation of 180 degrees about the point (2, 2).

   (a)

   Find the coordinates of X', Y' and Z'.

   [4 marks]

   (b)

   Triangle X'Y'Z' is then reflected in the line x = 2 to give triangle X''Y''Z''. Find the coordinates of X'', Y'' and Z''.

   [4 marks]

   (c)

   Describe fully the single transformation that maps triangle XYZ directly onto triangle X''Y''Z''.

   [5 marks]

   Total for question 4: 13 marks

End of questions