Transformations

GreenMaths, 1/9/2014

Tabla de Contenidos

  1. Axial Symmetry
    1. Axial symmetry - reflection in a line
    2. Facial Symmetry
    3. Reflection in the x-axis and y-axis
    4. Reflection in the line y = x
  2. Translations
    1. Translate a point
    2. Translate a triangle
  3. Central Symmetry
    1. Image of a Point by Central Symmetry
    2. Image of a Line Segment by Central Symmetry
    3. Image of a Triangle by Central Symmetry
    4. Playing Card and Central Symmetry
  4. Rotations
    1. Rotation Of An Object
    2. Rotation Of a point in steps of 90°
    3. Order of rotational symmetry for an equilateral triangle
    4. Order of rotational symmetry of regular polygons
    5. Playing card and rotational symmetry
    6. Escher's "Lizards" Tessellation
    7. Circles, Sectors and Area

1.

Axial Symmetry

Investigate axial symmetry (reflection in a line).

  • 1. Axial symmetry - reflection in a line
  • 2. Facial Symmetry
  • 3. Reflection in the x-axis and y-axis
  • 4. Reflection in the line y = x

1.1.

Axial symmetry - reflection in a line

Try yo work out where the image of the triangle will be first before you reveal the answer.[br]Move point D or E to move the line. Move a, B or C to change the shape of the triangle.
You can use the "polygon tool" to draw a triangle where you think the reflection will be. Click "Show Reflection" to check your drawing.[br][br]Use refresh to return to the start. Drag the points to move the triangle and the line and try different variations.
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2.

Translations

Investigate the translation of a point and of shapes.

  • 1. Translate a point
  • 2. Translate a triangle

2.1.

Translate a point

What is the image of A by the translation BC? Try to work out the answer before you use the slider to reveal it. [br][br]You can move the point A and the points B and C to change the translation.
Always predict the answer before you reveal it.
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2.2.

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3.

Central Symmetry

Investigate central symmetry (reflection in a point).

  • 1. Image of a Point by Central Symmetry
  • 2. Image of a Line Segment by Central Symmetry
  • 3. Image of a Triangle by Central Symmetry
  • 4. Playing Card and Central Symmetry

3.1.

Image of a Point by Central Symmetry

You can move the point A and the point O, which is the centre of symmetry. The "double translation" has the same effect as the central symmetry. Move A and O and work out the co-ordinates of the image first.

Try to work out the position of the image before you reveal the answer. Move both points and repeat.
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4.

Rotations

Investigate the rotation of points and shapes.

  • 1. Rotation Of An Object
  • 2. Rotation Of a point in steps of 90°
  • 3. Order of rotational symmetry for an equilateral triangle
  • 4. Order of rotational symmetry of regular polygons
  • 5. Playing card and rotational symmetry
  • 6. Escher's "Lizards" Tessellation
  • 7. Circles, Sectors and Area

4.1.

Rotation Of An Object

Drag the red point to rotate the triangle around the point O. Switch on trace to see the path of each point. Use the button to clear the trace.
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Información