Checking and securing understanding of translation | Maths

Starter quiz

A transformation is a process that may change the size, orientation or ______ of a shape.

'position' ✓
Select the pieces of information that are required to fully describe a rotation.

angle ✓

centre ✓

direction ✓

position

size
Shape c has been rotated 180°clockwise about (-2, 2). The image is shape ______.

'a' ✓
Match together equivalent rotations.

90° clockwise

⇔

270° anti-clockwise ✓

360° clockwise

⇔

720° anti-clockwise ✓

270° anti-clockwise

⇔

450° clockwise ✓

180° anti-clockwise

⇔

180° clockwise ✓
Shape ______ is congruent to shape A.

'B' ✓
Select the correct statements.

Shape d has been rotated 90° clockwise about (-2, 2). The image is shape c.

Shape d has been rotated 90° anti-clockwise about (-2, 2). The image is shape c. ✓

Shape d has been rotated 180° clockwise about (-2, 2). The image is shape a.

Shape b has been rotated 90° clockwise about (-2, 2). The image is shape a.

Shape b has been rotated 270° clockwise about (-2, 2). The image is shape a. ✓

Exit quiz

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

'translation' ✓
Select the diagrams that show a translation.
Match each description to the correct vector.

2 left and 3 down

⇔

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

2 right and 3 up

⇔

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

3 left and 2 up

⇔

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

3 right and 2 down

⇔

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

2 left and 3 up

⇔

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

3 right and 2 up

⇔

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

A is translated by $\begin{pmatrix} 4 \\ 1 \\ \end{pmatrix}$ onto D ✓

D is translated by $\begin{pmatrix} 2 \\ 1 \\ \end{pmatrix}$ onto F

F is translated by $\begin{pmatrix} -2 \\ 2 \\ \end{pmatrix}$ onto E ✓

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

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

Worksheet

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Lesson Details

Key learning points

It can be helpful to choose a vertex and translate that.
Once all the vertices have been translated, the image can be drawn.
The image and the object should be congruent.
To translate, you need to know the distance left/right and up/down to move.

Common misconception

Pupils may write or read the column vector incorrectly by thinking the top element is for the vertical movement and the bottom element is for the horizontal movement.

Remind pupils that coordinates are horizontal before vertical and that is the same on a column vector.

Keywords

Transformation - A transformation is a process that may change the size, orientation or position of a shape.
Translation - Translation is a transformation in which every point of a shape moves the same distance in the same direction.
Vector - A vector can be used to describe a translation.
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.