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Geometry : Key Stage 4 : Mathematics Content Knowledge

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Key Stage 4
Question 2 of 22

2. How confident are you that you understand through practical activity and the use of ICT the meaning of

a. translation?


Translation is a transformation in which every point of an object moves the same distance in the same direction. If a translation is on a coordinate grid, the moves parallel to the x-axis and parallel to the y-axis must be specified.


A transformation of a units parallel to the x-axis and b units parallel to the y-axis is written as a vector \left[a\\b

In three dimensions, a transformation of a units parallel to the x-axis, b units parallel to the y-axis and c units parallel to the z-axis is written as the vector \left[a\\b\\c

A translation has these properties:

  • The object and image are congruent.
  • The orientations of the original and the image are the same.
  • The inverse of any translation is an equal move in the opposite direction.

Dynamic geometry packages let you define a vector associated with a translation. By changing the vector and seeing how the translated image moves, and that the size, shape and orientation of the image never change no matter how the vector is changed help pupils to get a firm grasp of the properties of the translation.


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