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| Demonstration Pages for both JuniorMathsOnline and SeniorMathsOnline |
SeniorMathsOnline
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JuniorMathsOnline
- Percentages - example of notes with interactive tutorials.
- Transformations - animations of the common transformations of reflections, rotation, translation and enlargement.
- Vectors - notes including a simulation and a game.
- Trigonometry - simulation showing the sine as a circular function.
- Solid Shapes - pop-up windows describing various shapes.
- Algebra Crossnumber - learning algebra through crosswords.
- Expressions Test - one of the 355 multiple-choice topic tests.
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For a full list of each year's topics click the appropriate link below:
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Transformations
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The four transformations; reflection, rotation,
translation and enlargement are studied in more detail
in Year 9 and Year 11.
Download these documents for a look at this topic.
Below is a summary of each:
Reflection
When a shape or point is reflected its image is on
the opposite side of a mirror line or axis of symmetry.
The mirror line is halfway between the shape and its image.
The axis of symmetry is often shown by the letter m.
The object and the image are congruent, the same shape
and size.
Length, angle size and shape are said to be invariant for
reflection, which means they do not change.
Examples of reflections - 
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The diagram shows a reflection in the mirror line m
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Rotation
A rotation is a transformation where a point, or an
object, is turned around a fixed point to a new position called
the image.
The object and the image are the same shape
and the same size but in different positions.
When a shape or point is rotated there
is a centre of rotation which remains fixed.
The angle of rotation gives the number
of degrees that the shape is rotated through.
An anti-clockwise rotation is said to be positive.
A clockwise rotation is said to be
negative.
Examples of rotations -
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The diagram shows an anti-clockwise quarter
turn rotation about the centre of rotation, O.
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Translation
A translation is a transformation
where all points move the same distance and in the same direction.
The object and the image are the same shape and the
same size.
Translations can be represented by vectors.
In general the vector  can
represent a translation where x
is the horizontal movement and y is the vertical
movement.
Examples of translations -
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The diagram shows a translation of
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Enlargement
An enlargement is a transformation where the size
of an object changes.
Examples of enlargements -
The object becomes larger or smaller.
If points on the object and the corresponding points on the
image are joined with a straight line, these straight lines
meet at the centre of enlargement.
The scale factor for an enlargement tells how much
an object has been enlarged by.
A negative scale factor means the object and the image
are on opposite sides of the centre of enlargement.
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The diagram shows an enlargement, centre O with a
scale factor of 2.
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Download these files for more help with transformations:
| An interactive spreadsheet of reflections, rotations,
translations and enlargements. (Excel) |
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| A explanation about Transformations (Powerpoint). |
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| A worksheet on Reflection (Word). |
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| A worksheet on Rotation (Word). |
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(Windows users, right click and "Save target as..." to save
the files on your computer. When these files have been downloaded to your
computer you will need to use Microsoft Word, Excel and Microsoft PowerPoint
to open them.)
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