KS3 Maths · Year 7 · Chapter 2: Geometry · Lesson 3

Translations

Year 7About 70 minutesNo calculator45 marks

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Date

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Quick questions to start.

A1
Needed today
Work out $- 4 - 7$ .
[1 mark]
Answer
A2
Needed today
Which of these two points is further to the right: $(- 5, 3)$ or $(- 2, 3)$ ?
[1 mark]
Answer
A3
Last lesson
One angle of a parallelogram is $6 4^{\circ}$ . Work out the size of an angle next to it.
[1 mark]
Answer
A4
From chapter 1
Work out $(- 3)^{3}$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Describe the translation that takes shape $A$ onto shape $B$ .

Hint Pick one corner of

A

. Count the squares across to the same corner of

B

, then the squares up or down.

B1
Describe the translation that takes shape $C$ onto shape $D$ .
[2 marks]
Answer

Example 2

Translate the triangle $2$ units right and $1$ unit up. Write down the coordinates of the corners of the image.

Hint Move each corner on its own. Right adds to

x

, up adds to

y

B2
Translate the triangle $3$ units right and $2$ units down. Write down the coordinates of the corners of the image.
[2 marks]
Answer

Example 3

A point $Q$ is translated $4$ units left and $2$ units up. Its image is $(1, 6)$ . Find the coordinates of $Q$ .

Hint Undo the translation: go

4

units right and

2

units down from the image.

B3
A point $R$ is translated $5$ units right and $6$ units down. Its image is $(- 3, 2)$ . Find the coordinates of $R$ .
[2 marks]
Answer

Example 4

A shape is translated $3$ units right and $4$ units up. Its image is then translated $5$ units left and $1$ unit up. Describe the single translation that has the same effect.

Hint Add the moves across, with left counting as negative. Then add the moves up and down.

B4
A shape is translated $6$ units right and $2$ units down. Its image is then translated $1$ unit left and $5$ units down. Describe the single translation that has the same effect.
[2 marks]
Answer

Practice

Year 7

C1
Describe the translation that takes shape $F$ onto shape $E$ .
[2 marks]
Answer
C2
The point $(- 1, - 4)$ is translated $3$ units left and $6$ units up. Write down the coordinates of the image.
[2 marks]
Answer

C3
The translation $3$ units left and $2$ units up is written as the column vector $(- 3 2)$ . Write the translation $4$ units right and $5$ units down as a column vector.
[1 mark]
Answer
C4
The square is translated so that corner $K$ moves to $K^{'}$ . Write down the coordinates of the image of the corner $(3, 3)$ .
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Mia says, "The translation $4$ units right and $1$ unit down takes shape $A$ onto shape $B$ . So the same translation takes shape $B$ back onto shape $A$ ."
Mia is wrong. Explain why, and describe the translation that takes $B$ onto $A$ .
[3 marks]

D2
A robot on a coordinate grid starts at $(2, 1)$ . It makes three moves, one after the other: $3$ units right and $4$ units up, then $5$ units left and $2$ units down, then $1$ unit right and $6$ units down.
(a)
Work out the coordinates of the point where the robot finishes.
[2 marks]
Answer
(b)
Describe the single translation that takes the robot from where it finishes back to $(2, 1)$ .
[2 marks]
Answer
Total for D2: 4 marks
D3
Triangle $P$ is drawn on the grid.
(a)
$P$ is translated $5$ units right and $3$ units down to give triangle $Q$ . Write down the corners of $Q$ .
[2 marks]
Answer
(b)
$Q$ is translated $4$ units left and $1$ unit down to give triangle $R$ . Write down the corners of $R$ .
[2 marks]
Answer
(c)
Describe the single translation that takes triangle $R$ back onto triangle $P$ .
[2 marks]
Answer
Total for D3: 6 marks
D4
The point $K$ is translated by the column vector $(- 3 5)$ . Its image is $K^{'} = (1, 2)$ .
(a)
Work out the coordinates of $K$ .
[2 marks]
Answer
(b)
$K^{'}$ is then translated by the column vector $(6 - 2)$ to give $K^{''}$ . Write down the single column vector that translates $K$ to $K^{''}$ .
[2 marks]
Answer
Total for D4: 4 marks
D5
Triangle $T$ has corners $(1, 1)$ , $(4, 1)$ and $(1, 5)$ .
(a)
Work out the area of triangle $T$ .
[2 marks]
Answer
(b)
$T$ is translated $5$ units left and $2$ units down. Write down the area of the image. Give a reason.
[2 marks]
Answer
Total for D5: 4 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A translation moves rectangle $S$ to a new position on whole squares, still completely on this grid. How many different translations are there?
[5 marks]
Hint 1 · What to try
Work out how far right $S$ can move, and how far up, without leaving the grid.
Hint 2 · The first line
$S$ can move $0$ , $1$ , $2$ , $3$ or $4$ units right and $0$ , $1$ or $2$ units up.
Hint 3 · The full method
That is $5 \times 3 = 15$ positions. One is where $S$ already is, so there are $15 - 1 = 14$ translations.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can describe a translation in words and as a column vector.
I can translate a shape or a point, and undo a translation.
I can join two translations into one.

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