Checking and securing understanding of reflection | Maths

Starter quiz

A translation is a ______ in which every point of a shape moves the same distance in the same direction.

'transformation' ✓
Match each description to the correct vector.

4 left and 5 down

⇔

$\begin{pmatrix} -4 \\ -5 \\ \end{pmatrix}$ ✓

4 right and 5 up

⇔

$\begin{pmatrix} 4 \\ 5 \\ \end{pmatrix}$ ✓

5 left and 4 up

⇔

$\begin{pmatrix} -5 \\ 4 \\ \end{pmatrix}$ ✓

5 right and 4 down

⇔

$\begin{pmatrix} 5 \\ -4 \\ \end{pmatrix}$ ✓

4 left and 5 up

⇔

$\begin{pmatrix} -4 \\ 5 \\ \end{pmatrix}$ ✓

5 right and 4 up

⇔

$\begin{pmatrix} 5 \\ 4 \\ \end{pmatrix}$ ✓
The point P(4, 3) is translated by the vector $\begin{pmatrix} -2 \\ 1 \\ \end{pmatrix}$ to P'. What are the coordinates of P'?

(6, 4)

(2, 2)

(8, 6)

(6, 2)

(2, 4) ✓
Shape P is translated onto shape Q by the vector $\begin{pmatrix} -3 \\ 2\\ \end{pmatrix}$ . What transformation will map shape Q onto shape P?

Translation by $\begin{pmatrix} -3 \\ 2 \\ \end{pmatrix}$

Translation by $\begin{pmatrix} 3 \\ -2 \\ \end{pmatrix}$ ✓

$\begin{pmatrix} 2 \\ 3 \\ \end{pmatrix}$

$\begin{pmatrix} -2 \\ 3 \\ \end{pmatrix}$

$\begin{pmatrix} 2 \\ -3 \\ \end{pmatrix}$
Select the correct statements.

B is translated by $\begin{pmatrix} 0 \\ 2 \\ \end{pmatrix}$ onto C

C is translated by $\begin{pmatrix} 1 \\ -2 \\ \end{pmatrix}$ onto D ✓

D is translated by $\begin{pmatrix} 1 \\ 3 \\ \end{pmatrix}$ onto E ✓

E is translated by $\begin{pmatrix} -1 \\ -1\\ \end{pmatrix}$ onto F

F is translated by $\begin{pmatrix} -7 \\ -2\\ \end{pmatrix}$ onto A ✓
Match each line to its equation.

Line A

⇔

$x$ = -3 ✓

Line B

⇔

$y$ = 2 ✓

Line C

⇔

$y$ = $x$ ✓

Line D

⇔

$x$ = 2 ✓

Line E

⇔

$y$ = -3 ✓

Exit quiz

A reflection of a shape is the ______ image of the shape.

'mirror' ✓
Which of these diagrams show a reflection?
The line of reflection is Line ______.

'C' ✓
Shape A is reflected onto shape B. What is the equation of the line of reflection?

$x= 1$ ✓

$y = 1$

$x+y = 1$

$x-y=1$
Describe this transformation fully.

A rotation of 180° about the origin

A translation by the vector $\begin{pmatrix} 3 \\ -3 \\ \end{pmatrix}$

A reflection in the line $y=-x$

A reflection in the line $y=x$ ✓

A rotation of 180° clockwise about the origin
The point $P$ has coordinates $(3, -2)$ . $P$ is reflected in different lines of reflection. Match the coordinates of the image of $P$ to the equation of the line of reflection.

$P'(3, 2)$

⇔

$y = 0$ ✓

$P'(-3, -2)$

⇔

$x= 0$ ✓

$P'(-2, 3)$

⇔

$y=x$ ✓

$P'(2, -3)$

⇔

$y=-x$ ✓

Worksheet

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Lesson Details

Key learning points

The line of reflection can be vertical/horizontal/diagonal.
The line of reflection may go through part of the object.
The line of reflection may not touch the object.
To reflect, you need a line to reflect in.

Common misconception

Pupils may find reflecting across a diagonal line more challenging than vertically or horizontally.

Pupils may find it easier with tracing paper, or rotating their book/paper so the line of reflection is vertical.

Keywords

Transformation - A transformation is a process that may change the size, orientation or position of a shape.
Reflection - A reflection of a shape is the mirror image of the shape. An object is reflected when it is flipped over a fixed line (line of reflection), without the image being turned or its size changing.
Line of reflection - The line of reflection is the fixed line about which an object is reflected. The object and image are equidistant from the line of reflection.
Object - The object is the starting figure, before a transformation has been applied.
Image - The image is the resulting figure, after a transformation has been applied.