Transformations – Year 11 GCSE maths test answers to download as PDF

← Back to the test

1. Answer to Question 1 (4 marks)

   1. \((-2,1)\), \((-5,1)\), \((-2,4)\) (2: 1 for two correct) Reflecting in the \(y\)-axis changes the sign of each \(x\)-coordinate and keeps \(y\) the same.
   2. \((1,2)\), \((1,5)\), \((4,2)\) (2: 1 for two correct) Reflecting in the line \(y=x\) swaps the \(x\)- and \(y\)-coordinates of each vertex.

   In (a), a common error is to change the sign of \(y\), which reflects in the \(x\)-axis instead. In (b), the vertex \((2,1)\) becomes \((1,2)\), and a vertex on the line \(y=x\) would not move.

2. Answer to Question 2 (4 marks)

   1. \(\overrightarrow{CP}=(4,2)\) (1); clockwise \((x,y)\to(y,-x)\) gives \((2,-4)\) (1); image \(=\) \((3,-3)\) (1) Find the vector from the centre to \(P\), turn it with the clockwise rule, then add it back to the centre: \((1+2,1-4)\).
   2. Both distances \(\sqrt{16+4}=\sqrt{20}\) (1) A rotation does not change the distance from the centre: both vectors have length \(\sqrt{20}\).

   An anticlockwise rotation would give \((-1,5)\) instead, a common error.

3. Answer to Question 3 (4 marks)

   1. \(A'=(1,1)+2(1,1)=(3,3)\); \(B'=(1,1)+2(3,1)=(7,3)\); \(C'=(1,1)+2(1,4)=(3,9)\) (1 each) For each vertex, find the vector from the centre \((1,1)\), double it, and add it to the centre. The image is twice as far from the centre as the original.
   2. \(3\times4=\) 12 (1) The area scale factor is the square of the length scale factor, \(2^2=4\).

   In (a), a common error is to double the coordinates directly, which uses the origin as the centre.

4. Answer to Question 4 (4 marks)

   1. Rotation (1), \(180^\circ\) (1), about the origin (1) Every coordinate changes sign, which is a half turn: rotation of \(180^\circ\) about \((0,0)\). A full description must give the type, the angle and the centre.
   2. Enlargement with scale factor \(-1\) and centre the origin (1) An enlargement with scale factor \(-1\) about the origin also changes the sign of every coordinate, so it gives the same image.

5. Answer to Question 5 (4 marks)

   1. \((-9,-3)\) (2) With centre the origin, multiply both coordinates by \(-3\): \(3\times(-3)=-9\) and \(1\times(-3)=-3\). The image is on the opposite side of the origin.
   2. \(10\times(-3)^2=\) 90 cm² (2) The area scale factor is the square of the scale factor, and \((-3)^2=9\) is positive, so the area becomes 90 cm².

   A negative scale factor also turns the shape upside down, like a rotation of \(180^\circ\) combined with an enlargement of scale factor 3.

Total : 20 marks