Translations and dilations

Translate shapes using vectors and dilate shapes from the origin using a scale factor.

Worked examples

Translating a point using a vector

Straightforward

Problem

Translate point

A(2, 5)

by the vector

\begin{pmatrix} 3 \\ -4 \end{pmatrix}

and state the coordinates of

A'

Dilating a point from the origin

Moderate

Problem

Point

B(4, -2)

is dilated from the origin by scale factor

3

. State the coordinates of

B'

Finding the scale factor and classifying a dilation

Challenging

Problem

Point

C(5, 10)

is mapped to

C'(2, 4)

by a dilation from the origin. Find the scale factor and classify the transformation as an enlargement, reduction or congruent.

Practise

Q1·Straightforward

Point

A(3, 2)

is translated by the vector

\begin{pmatrix} 4 \\ -1 \end{pmatrix}

. State the coordinates of

A'

Q2·Straightforward

Point

B(-2, 5)

is translated by the vector

\begin{pmatrix} 3 \\ -4 \end{pmatrix}

. State the coordinates of

B'

Q3·Straightforward

Point

C(0, -3)

is translated by the vector

\begin{pmatrix} -2 \\ 6 \end{pmatrix}

. State the coordinates of

C'

Q4·Straightforward

A rectangle has vertex

D(5, -1)

. It is translated by the vector

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

. State the coordinates of

D'

Q5·Moderate

Point

E(3, 4)

is dilated from the origin by scale factor

2

. State the coordinates of

E'

Q6·Moderate

Point

F(-2, 5)

is dilated from the origin by scale factor

3

. State the coordinates of

F'

Q7·Moderate

Triangle has vertex

G(6, -4)

. It is dilated from the origin by scale factor

\dfrac{1}{2}

. State the coordinates of

G'

Q8·Moderate

Point

H(-4, 6)

is dilated from the origin by scale factor

\dfrac{3}{2}

. State the coordinates of

H'

Q9·Challenging

Point

P(3, 5)

is mapped to

P'(6, 10)

by a dilation from the origin. What is the scale factor?

Q10·Challenging

Point

Q(4, 8)

is mapped to

Q'(1, 2)

by a dilation from the origin. What is the scale factor?

Q11·Challenging

Point

R(-6, 9)

is mapped to

R'(-2, 3)

by a dilation from the origin. What is the scale factor?

Q12·Challenging

Triangle

ABC

has side lengths

3

cm,

4

cm and

5

cm. It is mapped to triangle

A'B'C'

with side lengths

6

cm,

8

cm and

10

cm. Classify this transformation.

EnlargementReductionCongruentReflection

Open Math

Translations and dilations

Space · MA4-GEO-C-01

Name:

Date:

Q1Straightforward

Point

A(3, 2)

is translated by the vector

\begin{pmatrix} 4 \\ -1 \end{pmatrix}

. State the coordinates of

A'

Q2Straightforward

Point

B(-2, 5)

is translated by the vector

\begin{pmatrix} 3 \\ -4 \end{pmatrix}

. State the coordinates of

B'

Q3Straightforward

Point

C(0, -3)

is translated by the vector

\begin{pmatrix} -2 \\ 6 \end{pmatrix}

. State the coordinates of

C'

Q4Straightforward

A rectangle has vertex

D(5, -1)

. It is translated by the vector

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

. State the coordinates of

D'

Q5Moderate

Point

E(3, 4)

is dilated from the origin by scale factor

2

. State the coordinates of

E'

Q6Moderate

Point

F(-2, 5)

is dilated from the origin by scale factor

3

. State the coordinates of

F'

Q7Moderate

Triangle has vertex

G(6, -4)

. It is dilated from the origin by scale factor

\dfrac{1}{2}

. State the coordinates of

G'

Q8Moderate

Point

H(-4, 6)

is dilated from the origin by scale factor

\dfrac{3}{2}

. State the coordinates of

H'

Q9Challenging

Point

P(3, 5)

is mapped to

P'(6, 10)

by a dilation from the origin. What is the scale factor?

Q10Challenging

Point

Q(4, 8)

is mapped to

Q'(1, 2)

by a dilation from the origin. What is the scale factor?

Q11Challenging

Point

R(-6, 9)

is mapped to

R'(-2, 3)

by a dilation from the origin. What is the scale factor?

Q12Challenging

Triangle

ABC

has side lengths

3

cm,

4

cm and

5

cm. It is mapped to triangle

A'B'C'

with side lengths

6

cm,

8

cm and

10

cm. Classify this transformation.

A.Enlargement
B.Reduction
C.Congruent
D.Reflection

Worked solutions and answers at openmath.au/year-8/properties-of-geometrical-figures/translations-and-dilations