Properties of geometrical figures

Perform and describe reflections, rotations, translations and dilations.

Space · MA4-GEO-C-01

Sub-topics

Reflections and rotations

Reflect points and shapes in the x-axis or y-axis, rotate points 90° and 180° about the origin, and identify transformations from original and image coordinates.

Translations and dilations

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

Open Math

Properties of geometrical figures

Space · MA4-GEO-C-01

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Date:

Reflections and rotations

Q1Straightforward

Reflect the point

A(3, 2)

in the

x

-axis. State the new coordinates.

Q2Straightforward

Reflect the point

B(-4, 1)

in the

y

-axis. State the new coordinates.

Q3Straightforward

Reflect the point

C(5, -3)

in the

x

-axis. State the new coordinates.

Q4Straightforward

Reflect the point

D(-2, -6)

in the

y

-axis. State the new coordinates.

Q5Moderate

Rotate the point

P(3, 4)

90°

anticlockwise about the origin. State the new coordinates.

Q6Moderate

Rotate the point

Q(2, -5)

180°

about the origin. State the new coordinates.

Q7Moderate

Rotate the point

R(-3, 4)

90°

clockwise about the origin. State the new coordinates.

Q8Moderate

Rotate the point

S(6, -2)

90°

anticlockwise about the origin. State the new coordinates.

Q9Challenging

The point

A(3, -4)

maps to

A'(-3, -4)

. Which transformation was applied?

A.Reflection in the $x$ -axis
B.Reflection in the $y$ -axis
C.Rotation of $90°$ anticlockwise about the origin
D.Rotation of $180°$ about the origin

Q10Challenging

The point

Q(-5, 2)

maps to

Q'(2, 5)

. Which transformation was applied?

A.Reflection in the $x$ -axis
B.Reflection in the $y$ -axis
C.Rotation of $90°$ anticlockwise about the origin
D.Rotation of $90°$ clockwise about the origin

Q11Challenging

The point

R(4, -3)

maps to

R'(-4, 3)

. Which transformation was applied?

A.Reflection in the $x$ -axis
B.Reflection in the $y$ -axis
C.Rotation of $90°$ clockwise about the origin
D.Rotation of $180°$ about the origin

Q12Challenging

The point

S(2, 6)

maps to

S'(-6, 2)

. Which transformation was applied?

A.Reflection in the $x$ -axis
B.Reflection in the $y$ -axis
C.Rotation of $90°$ anticlockwise about the origin
D.Rotation of $90°$ clockwise about the origin

Translations and dilations

Q13Straightforward

Point

A(3, 2)

is translated by the vector

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

. State the coordinates of

A'

Q14Straightforward

Point

B(-2, 5)

is translated by the vector

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

. State the coordinates of

B'

Q15Straightforward

Point

C(0, -3)

is translated by the vector

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

. State the coordinates of

C'

Q16Straightforward

A rectangle has vertex

D(5, -1)

. It is translated by the vector

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

. State the coordinates of

D'

Q17Moderate

Point

E(3, 4)

is dilated from the origin by scale factor

2

. State the coordinates of

E'

Q18Moderate

Point

F(-2, 5)

is dilated from the origin by scale factor

3

. State the coordinates of

F'

Q19Moderate

Triangle has vertex

G(6, -4)

. It is dilated from the origin by scale factor

\dfrac{1}{2}

. State the coordinates of

G'

Q20Moderate

Point

H(-4, 6)

is dilated from the origin by scale factor

\dfrac{3}{2}

. State the coordinates of

H'

Q21Challenging

Point

P(3, 5)

is mapped to

P'(6, 10)

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

Q22Challenging

Point

Q(4, 8)

is mapped to

Q'(1, 2)

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

Q23Challenging

Point

R(-6, 9)

is mapped to

R'(-2, 3)

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

Q24Challenging

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