GCSE Higher Ch8 Transformations & Constructions

Nicola Trubridge, May 2, 2018

Table of Contents

  1. Reflections
    1. Reflection in the x axis
    2. Reflection in the y axis
    3. Reflection in the line y=x
    4. Reflection: Find the mirror line (NJT)
    5. Reflection: Find the mirror line task 2 (NJT)
    6. EXTENSION: Reflection in y=mx (NJT)
    7. Test yourself: Reflection
    8. Exploring Reflections
  2. Rotations
    1. Rotation of 0-360 degrees around a centre (NJT)
    2. Rotation: Find the centre task 1 (NJT)
    3. Rotation: Find the centre task 2 (NJT)
    4. Rotation: Find the centre task 3 (NJT)
    5. Test yourself: Rotation
  3. Enlargements
    1. Enlargement Positive integer SF (NJT)
    2. Enlargement: Find the centre 1(NJT)
    3. Enlargement: Find the centre 2(NJT)
    4. Enlargement: Find the centre 3 (NJT)
    5. Enlargement Positive Fractional SF (NJT)
    6. Enlargement Negative and Fractional SF (NJT)
  4. Translations
    1. Translation 1 (NJT)
  5. Combined transformations
    1. 'Tangram' Puzzle 'Cat'
    2. rotation ?
    3. Transformations: Exercise 1
    4. Transformations: Exercise 3
    5. Transformations: Exercise 2
  6. Bearings
    1. Bearings 1
    2. Bosnian Bearings
    3. Bearings (True and Compass)
    4. Copy of Quiz on Compass Bearings
    5. Bearings -Test yourself
    6. Bearings Map of Europe
  7. Constructions
    1. Angle Bisector Definition (I)
    2. Angle Bisector: Construction
    3. Equilateral Triangle Construction Template
    4. Circumcentre and Circumcircle of a Circle
    5. In-centre, Circumcentre, Centroid and Orthocentre.
    6. Where's Waldo? (I)
  8. Loci
    1. Circles?
    2. HW question locus 1
    3. HW question locus 2
    4. HW question locus 3
    5. HW question locus 4
    6. HW question locus 5
    7. HW question locus 6
    8. Rolling Square
    9. Rolling a Regular Polygon
    10. Generalized Rolling Polygon
    11. Rolling Coin
    12. Rolling on the inside
    13. Mechanical loci
    14. Locus Problem (1)

1.

Reflections

  • 1. Reflection in the x axis
  • 2. Reflection in the y axis
  • 3. Reflection in the line y=x
  • 4. Reflection: Find the mirror line (NJT)
  • 5. Reflection: Find the mirror line task 2 (NJT)
  • 6. EXTENSION: Reflection in y=mx (NJT)
  • 7. Test yourself: Reflection
  • 8. Exploring Reflections

1.1.

Reflection in the x axis

What stays the [b]same[/b] and what [b]changes[/b] as you move the points around?[br]Are there any points that do not move under this transformation?[br]Where would the co-ordinate (x,y) map to?
[color=#0a971e]Created by N.Trubridge[/color]
What happens
– Nicola Trubridge

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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2.

Rotations

  • 1. Rotation of 0-360 degrees around a centre (NJT)
  • 2. Rotation: Find the centre task 1 (NJT)
  • 3. Rotation: Find the centre task 2 (NJT)
  • 4. Rotation: Find the centre task 3 (NJT)
  • 5. Test yourself: Rotation

2.1.

Rotation of 0-360 degrees around a centre (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move [list] [*]the slider? [*]the vertices B,C and D? [*]the centre of rotation? [/list] Are there any points that do not move under this transformation?

[color=#0a971e]Created by N.Trubridge[/color]
– Nicola Trubridge

2.2.

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2.3.

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2.4.

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2.5.

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3.

Enlargements

  • 1. Enlargement Positive integer SF (NJT)
  • 2. Enlargement: Find the centre 1(NJT)
  • 3. Enlargement: Find the centre 2(NJT)
  • 4. Enlargement: Find the centre 3 (NJT)
  • 5. Enlargement Positive Fractional SF (NJT)
  • 6. Enlargement Negative and Fractional SF (NJT)

3.1.

Enlargement Positive integer SF (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move[br][list][br][*]the SF slider[br][*]the centre[br][*]the vertices A,B and C?[br][/list][br]Are there any points that do not move under this transformation?
[color=#0a971e]Created by N.Trubridge[/color]
– Nicola Trubridge

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4.

Translations

  • 1. Translation 1 (NJT)

4.1.

Translation 1 (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move [list] [*]the vertices of the polygons? [*]the polygons? [*]the vector? [*]the ends of the vector? [/list] Do any points stay in the same place after this transformation?

[color=#0a971e]Created by N.Trubridge[/color]
– Nicola Trubridge

5.

Combined transformations

  • 1. 'Tangram' Puzzle 'Cat'
  • 2. rotation ?
  • 3. Transformations: Exercise 1
  • 4. Transformations: Exercise 3
  • 5. Transformations: Exercise 2

5.1.

'Tangram' Puzzle 'Cat'

Use all geometric shapes below in order to recreate the cat shown. You can translate the shapes by dragging the blue points. You can rotate the shapes by dragging the green points with the mouse. Click the little icon in the upper right corner in order to reset the worksheet and start over.
– GeoGebra Translation Team German

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5.5.

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6.

Bearings

  • 1. Bearings 1
  • 2. Bosnian Bearings
  • 3. Bearings (True and Compass)
  • 4. Copy of Quiz on Compass Bearings
  • 5. Bearings -Test yourself
  • 6. Bearings Map of Europe

6.1.

Bearings 1
– ishakfajar

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6.4.

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6.5.

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6.6.

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7.

Constructions

  • 1. Angle Bisector Definition (I)
  • 2. Angle Bisector: Construction
  • 3. Equilateral Triangle Construction Template
  • 4. Circumcentre and Circumcircle of a Circle
  • 5. In-centre, Circumcentre, Centroid and Orthocentre.
  • 6. Where's Waldo? (I)

7.1.

Angle Bisector Definition (I)

[color=#000000]In the applet below, the [/color][b][color=#1e84cc]blue ray[/color][/b][color=#000000] is said to be an [/color][color=#1e84cc][b]angle bisector[/b][/color][color=#000000] of [/color][b]angle [i]BAC[/i][/b][color=#000000]. [br][br]The [/color][b]gray slider[/b][color=#000000] adjusts the entire measure of [/color][b]angle [i]BAC[/i][/b][color=#000000]. [br][/color][color=#000000]The [b]black slider[/b] dynamically illustrates what it means for a [/color][color=#1e84cc][b]ray[/b][/color][color=#000000] to [/color][color=#1e84cc][b]bisect[/b][/color][color=#000000] an angle. [br][br][/color][color=#000000]Interact with this applet for a few minutes. [br]Then, answer the questions that follow. [/color]
1.
[color=#000000]From what you've seen, describe what it means for a [/color][color=#1e84cc][b]ray[/b][/color][color=#000000] to [/color][color=#1e84cc][b]bisect[/b][/color][color=#000000] an angle. [br][/color][b][color=#ff00ff]In your description, avoid using the words or phrases "[i]middle", "down-the-middle", "half"[/i]. [/color][/b]
2.
[color=#000000]Use the [b]Point on Object[/b] tool to plot a point F [/color][color=#1e84cc]anywhere on the [b]angle bisector[/b][/color][color=#000000]. [br]Use the [b]Angle[/b] tool to find and display the measure of angle [/color][i]BAF[/i][color=#000000] and [/color][i]CAF[/i][color=#000000]. [br][/color][color=#000000][br]How do these results reflect (i.e. illustrate) your response to (1)? [/color]
Quick (Silent) Demo
– Tim Brzezinski

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8.

Loci

  • 1. Circles?
  • 2. HW question locus 1
  • 3. HW question locus 2
  • 4. HW question locus 3
  • 5. HW question locus 4
  • 6. HW question locus 5
  • 7. HW question locus 6
  • 8. Rolling Square
  • 9. Rolling a Regular Polygon
  • 10. Generalized Rolling Polygon
  • 11. Rolling Coin
  • 12. Rolling on the inside
  • 13. Mechanical loci
  • 14. Locus Problem (1)

8.1.

Circles?

Describe the motion you see.
Do you see straight lines? Is there a circular flavour?[br]Explore further by clicking 'show checkboxes'
– Ben Sparks

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8.5.

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8.6.

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8.7.

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8.8.

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8.9.

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8.10.

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8.11.

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8.12.

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8.13.

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8.14.

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Information