Exam-Style Problems

Stage 9 - Q1 - 4 marks

20017

Reflect ABC in \(x=0\), then translate by the vector.

\[\begin{pmatrix}2\\2\end{pmatrix}\]

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Object

A

B

C

Hint

Reflect first; apply the vector to the reflected vertices.

Stage 9 - Q2 - 4 marks

20018

Translate ABC by the vector, then reflect in \(y=-1\).

\[\begin{pmatrix}1\\2\end{pmatrix}\]

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Object

A

B

C

Hint

Translate first; reflect the translated vertices.

Stage 9 - Q3 - 4 marks

20019

Reflect ABC in \(x=0\), then \(x=3\). Find the image and describe one equivalent transformation.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Object

A

B

C

Hint

Track one x-coordinate through both reflections, then verify all vertices.

Stage 9 - Q4 - 4 marks

20020

Reflect ABC in \(x=0\), then translate by the vector.

\[\begin{pmatrix}2\\1\end{pmatrix}\]

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Object

A

B

C

Hint

Reflect first; apply the vector to the reflected vertices.

Stage 9 - Q5 - 4 marks

20021

For \(P=(-3,1)\), compare reflection in \(x=-1\) then translation \((1,1)\), with the reverse order.

Hint

Each second transformation acts on the new point.

Stage 9 - Q6 - 3 marks

20022

ABC is reflected in \(y=1\) then translated by \((3,3)\). State a sequence that returns the final image to ABC.

x

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

0

Object

Image

A

B

C

A'

B'

C'

Hint

Inverse operations are applied in reverse order.

Stage 9 - Q7 - 4 marks

20023

Translate ABC by the vector, then reflect in \(y=0\).

\[\begin{pmatrix}2\\3\end{pmatrix}\]

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Object

A

B

C

Hint

Translate first; reflect the translated vertices.

Stage 9 - Q8 - 4 marks

20024

Reflect ABC in \(x=1\), then \(x=5\). Find the image and describe one equivalent transformation.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Object

A

B

C

Hint

Track one x-coordinate through both reflections, then verify all vertices.

Stage 9 - Q9 - 4 marks

20025

For \(P=(0,-2)\), compare reflection in \(x=1\) then translation \((3,2)\), with the reverse order.

Hint

Each second transformation acts on the new point.

Stage 9 - Q10 - 6 marks

20026

A reflection in \(x=a\) is followed by a reflection in \(x=b\). Derive a single equivalent transformation. Then choose two mirror lines giving translation \((8,0)\).

Hint

Track an arbitrary x-coordinate through both reflection rules.