18.1 Reflection, rotation and translation — Practise

Work through these on your own. Questions marked H are for Higher only.

Reflect the point $(3,2)$ in the $y$ -axis. Give its image.
Rotate $(2,1)$ by $90^\circ$ clockwise about the origin.
Translate $(-1,3)$ by the vector $\begin{pmatrix}4\\-2\end{pmatrix}$ .
Describe the single transformation taking $(1,2)$ to $(-1,2)$ and $(3,2)$ to $(-3,2)$ .
Reflect $(4,-2)$ in the line $y=x$ .
Triangle vertices are $(0,0),(2,0),(1,3)$ . Translate by $\begin{pmatrix}-3\\1\end{pmatrix}$ . Give all image vertices.
Rotate $(4,2)$ by $180^\circ$ about the origin.
A shape keeps its size and orientation but moves three left and one up. A vertex at $(2,1)$ moves to $(-1,2)$ . Which transformation applies, and why?
Reflect $(-5,2)$ in the $x$ -axis.
Rotate $(1,-4)$ by $90^\circ$ anticlockwise about the origin.
H Translate the triangle with vertices $(1,1)$ , $(3,1)$ and $(1,2)$ by $\begin{pmatrix}1\\1\end{pmatrix}$ . Then reflect it in the $y$ -axis and rotate it $90^\circ$ clockwise about the origin. Give the image vertices and state what stays unchanged.

Answers and concise solutions

1. Reflect the point $(3,2)$ in the $y$ -axis. Give its image.

Answer: (-3,2)

2. Rotate $(2,1)$ by $90^\circ$ clockwise about the origin.

Answer: (1,-2)

3. Translate $(-1,3)$ by the vector $\begin{pmatrix}4\\-2\end{pmatrix}$ .

Answer: (3,1)

4. Describe the single transformation taking $(1,2)$ to $(-1,2)$ and $(3,2)$ to $(-3,2)$ .

Answer: Reflection in the $y$ -axis.

5. Reflect $(4,-2)$ in the line $y=x$ .

Answer: (-2,4)

6. Triangle vertices are $(0,0),(2,0),(1,3)$ . Translate by $\begin{pmatrix}-3\\1\end{pmatrix}$ . Give all image vertices.

Answer: (-3,1), (-1,1), (-2,4)

7. Rotate $(4,2)$ by $180^\circ$ about the origin.

Answer: (-4,-2)

8. A shape keeps its size and orientation but moves three left and one up. A vertex at $(2,1)$ moves to $(-1,2)$ . Which transformation applies, and why?

Answer: Translation by $\begin{pmatrix}-3\\1\end{pmatrix}$ ; every point moves by the same vector.

9. Reflect $(-5,2)$ in the $x$ -axis.

Answer: (-5,-2)

10. Rotate $(1,-4)$ by $90^\circ$ anticlockwise about the origin.

Answer: (4,1)

11. Translate the triangle with vertices $(1,1)$ , $(3,1)$ and $(1,2)$ by $\begin{pmatrix}1\\1\end{pmatrix}$ . Then reflect it in the $y$ -axis and rotate it $90^\circ$ clockwise about the origin. Give the image vertices and state what stays unchanged.

Answer: (2,2), (2,4), (3,2); side lengths and angles stay unchanged.