Worksheets · Foundation and Higher

Reflections, rotations and translations

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 3 marks

   This question is about translations.

   (a) The point $A(2, 5)$ is translated to the point $A'(6, 1)$. Write down the column vector of the translation. (1)

   (b) The point $B(-3, 2)$ is translated by the vector $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$. Write down the coordinates of the image of $B$. (1)

   (c) Write down the column vector that translates $A'$ back to $A$. (1)
2. Question 2Non-calculator · 4 marks

   Point A is $(2,-1)$. It is reflected in the line x = −1.

   (a) Find the coordinates of the image B. (2)

   (b) Find the translation vector mapping A to B. (2)
3. Question 3Non-calculator · 5 marks

   This question is about reflections.

   (a) The point $P(0, 6)$ is reflected in the line $L$. Its image is $P'(4, 2)$. Find an equation of the line $L$. (3)

   (b) Triangle $T$ has vertices $(2, 1)$, $(5, 1)$ and $(5, 3)$. Triangle $U$ has vertices $(-1, -2)$, $(-1, -5)$ and $(-3, -5)$. Describe fully the single transformation that maps $T$ onto $U$. (2)