Transformations & Symmetry

Draw the lines of symmetry on a square.

Draw the line of symmetry on a heart shape.

Draw the lines of symmetry on a regular hexagon.

Shape A is at (1, 2). Shape B is at (5, 2). Transformation: ___

Shape A faces left. Shape B faces right. Transformation: ___

Shape A is upright. Shape B is turned 90° clockwise. Transformation: ___

Shape A at (2, 1) moves to (2, 5). Transformation: ___

Shape A at (3, 3) becomes its mirror image across the y-axis. Transformation: ___

Shape A at (4, 2) turns 180° around its centre. Transformation: ___

Point (2, 3) moves to (5, 3). Translation: ___ right, ___ up

Point (4, 7) moves to (4, 2). Translation: ___ right, ___ down

Point (1, 1) moves to (6, 4). Translation: ___ right, ___ up

Draw a right-angled triangle. Then draw its reflection across a vertical line.

Draw an L-shape. Translate it 4 squares to the right and 2 squares up.

Draw a simple arrow pointing right. Then rotate it 90° clockwise.

Draw a rectangle at (1,1), (3,1), (3,2), (1,2). Reflect it across x = 4.

Draw a triangle at (1,1), (2,3), (3,1). Translate it 4 right and 2 up.

Draw the right half of a symmetric pattern on grid paper.

Draw the bottom half of a symmetric pattern (line of symmetry is horizontal).

If you reflect a shape twice across two parallel lines, what single transformation gives the same result?

Which capital letters look the same after a 180° rotation? List them.

Draw the lines of symmetry on an equilateral triangle.

Draw the lines of symmetry on a rectangle.

Draw the line of symmetry on an isosceles triangle.

List all capital letters with vertical symmetry: ___

List all capital letters with horizontal symmetry: ___

List all single-digit numbers with a line of symmetry: ___

Shape A at (1, 3) moves to (6, 3). Transformation: ___ ___ right

Shape A at (4, 2) moves to (4, 8). Transformation: ___ ___ up

Shape A faces right, shape B faces left (same position). Transformation: ___

Shape A is upright, shape B is rotated 90° anticlockwise. Transformation: ___

Point (1, 6) moves to (5, 2). Translation: ___ right, ___ down

Point (7, 1) moves to (3, 4). Translation: ___ left, ___ up

Point (0, 0) moves to (8, 5). Translation: ___ right, ___ up

A square: order of rotational symmetry = ___

An equilateral triangle: order = ___

A regular hexagon: order = ___

A rectangle (not square): order = ___

Draw a triangle at (1, 1), (3, 1), (2, 3). Rotate it 90° clockwise around (1, 1). Write the new coordinates.

Draw an L-shape. Reflect it across a vertical line. Then translate the reflection 3 units up.

Draw a rectangle at (0, 0), (4, 0), (4, 2), (0, 2). Reflect it across y = 3. Write new coordinates.

Draw an arrow pointing up at (3, 1). Rotate 90° clockwise, then 90° clockwise again. What direction does it point now?

Draw a pattern with exactly 2 lines of symmetry.

Draw a pattern with rotational symmetry of order 4.

Start with point (2, 1). Translate right 3, then reflect across x = 7. Final position: ___

Start with point (5, 3). Reflect across y = 4, then translate left 2. Final position: ___

Is the order of transformations important? Explain with an example.

Name 3 shapes that tessellate (tile a surface with no gaps): ___

Does a regular pentagon tessellate? Why or why not?

Draw a simple tessellation using triangles.

Regular pentagon: order ___

Regular octagon: order ___

A shape that looks the same every 120° has order ___

A shape with no rotational symmetry (other than 360°) has order ___

A shape moves from (1, 2) to (4, 6). Translation: right ___, up ___

A shape moves from (7, 5) to (3, 2). Translation: left ___, down ___

A shape moves from (0, 0) to (5, 3) to (5, 7). Describe as two translations: ___

Reflect (4, 2) across the vertical line x = 6: (__, __)

Reflect (1, 5) across the horizontal line y = 3: (__, __)

Reflect (3, 3) across the line y = x: (__, __)

Draw a simple shape. Translate it 3 times to create a repeating border pattern.

Draw a shape with 4-fold rotational symmetry (looks the same every 90°).

The Australian flag: does it have any line(s) of symmetry? ___

The letter 'H': how many lines of symmetry? ___. Order of rotational symmetry? ___

Name a logo or symbol that has rotational symmetry. Describe it.

Translate a triangle right 4. Then translate it up 3. What single translation gives the same result?

Rotate a shape 90° clockwise, then 90° clockwise again. What single rotation gives the same result?

Reflect a shape, then reflect it again across the same line. What do you get?

List capital letters with vertical symmetry (A, M, ...): ___

List capital letters with horizontal symmetry (B, C, ...): ___

List capital letters with both vertical and horizontal symmetry: ___

List capital letters with 180° rotational symmetry (looks same upside down): ___

Squares tessellate (tile with no gaps). Draw a 3×3 square tessellation.

Equilateral triangles tessellate. Draw a triangle tessellation.

Which regular polygon does NOT tessellate? Pentagon or hexagon? Explain.

A square with side 3 cm is enlarged by scale factor 2. New side: ___ cm. New area: ___

A rectangle 4 cm × 6 cm is enlarged by scale factor 3. New dimensions: ___ × ___

Is an enlargement the same type of transformation as translation, reflection or rotation? Why not?

A square at (0,0), (3,0), (3,3), (0,3) is reflected across x = 4. New corners: ___, ___, ___, ___

The same square is translated right 2, up 5. New corners: ___, ___, ___, ___

The original square is rotated 90° clockwise around (0,0). New corners: ___, ___, ___, ___

Name an Australian building with bilateral (line) symmetry: ___

Name a building with rotational symmetry: ___

Why do architects often use symmetry in building design?

Point (3, 4) translated by (−2, +3): new position ___

Point (5, 2) reflected over the x-axis: new position ___

Point (4, 0) rotated 90° clockwise around origin: new position ___

Point (2, 3) enlarged by scale factor 3 from origin: new position ___

Name 3 animals with bilateral (line) symmetry: ___, ___, ___

Name a naturally occurring shape with rotational symmetry: ___

Why might bilateral symmetry be useful for animals?

Draw an example of a natural pattern with 6-fold rotational symmetry:

Start with a simple shape. Describe how you would use translation to create a pattern:

How would you add reflection to make it more interesting?

Design the pattern in the space below:

A cube has how many planes of symmetry? ___

A cylinder has ___ planes of symmetry (infinite). A sphere has ___ planes of symmetry.

A rectangular prism (not a cube): how many planes of symmetry?

The artist M.C. Escher used tessellations in his work. What is a tessellation?

How are reflections used in Aboriginal art patterns?

Design a simple tessellating shape and show how it would tile:

Square with vertices (0,0), (3,0), (3,3), (0,3) translated (+4, +2). New vertices: ___

Triangle with vertices (1,1), (5,1), (3,4) translated (−2, −1). New vertices: ___

Is the image of a translation congruent to the original? ___. Why?

Reflect the point (4, 3) across the x-axis: ___. Across the y-axis: ___

A triangle has vertices (2, 1), (6, 1), (4, 5). After reflecting across the y-axis: ___

What happens to the shape's orientation after a reflection?

Start with point (3, 2). First translate (+2, −1), then reflect across x-axis. Final position: ___

Does the order of transformations matter? Test: translate first then reflect vs reflect first then translate. Do you get the same result?

A sunflower has 5-fold rotational symmetry. What angle is each rotation? ___

A snowflake has 6-fold rotational symmetry. What is each rotation angle? ___

Name another natural object with rotational symmetry and describe it:

A regular hexagon tessellates. Interior angle = 120°. 3 × 120° = 360°. Why does this matter? ___

A regular pentagon has interior angle 108°. Does it tessellate? 108 × ? = 360 → ___. Explain:

A square has rotational symmetry of order 4 (at 90°, 180°, 270°, 360°). Draw and label the rotation:

What order of rotational symmetry does a regular octagon have? ___. Rotation angle: ___°

Does a scalene triangle have any rotational symmetry? ___

A triangle has vertices at (1,2), (4,2), (1,5). Describe its reflection across the x-axis:

After rotating 90° clockwise around origin: (3,4) becomes ___

Create a tessellation of a simple quadrilateral on grid paper. Describe the transformation used:

Describe one type of symmetry often found in Australian Indigenous art patterns:

Why might symmetry be important in cultural art and design?

Design your own pattern using at least one transformation. Describe your transformation: