Mathematics

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Definitions about transformations.

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Mathematics

  1. 1. Mathematics Vectors & transformations
  2. 2. The four transformations <ul><li>T ranslation ONE Detail </li></ul><ul><li>E enlargement TWO Details </li></ul><ul><li>R otation THREE Details </li></ul><ul><li>R eflection ONE Detail </li></ul><ul><li>Y </li></ul>The word TERRY: only to remember the 4 types. You must specify all the details for each type.
  3. 3. TRANSLATION <ul><li>Translation is the movement of an object over a specified distance along a line. </li></ul><ul><li>The object is not twisted or turned. </li></ul><ul><li>The image is congruent to the object that was transformed. </li></ul><ul><li>You must specify one detail: the vector of translation. </li></ul>
  4. 4. ENLARGEMENT <ul><li>Enlargement is a transformation in which each point of an object is mapped along a straight line drawn from a fixed point. </li></ul><ul><li>You must specify two details: the scale factor and the centre of enlargement. </li></ul><ul><li>A scale factor greater then 1 enlarges the object. </li></ul><ul><li>A scale factor smaller than 1 reduces the object. </li></ul>
  5. 5. ROTATION <ul><li>Rotation occurs when an object is turned around a given point. </li></ul><ul><li>You must specify three details: angle turned, direction (clockwise or anti-clockwise) and centre of rotation. </li></ul><ul><li>The object and the image are congruent. </li></ul>
  6. 6. REFLECTION <ul><li>A reflection is a transformation in which any two corresponding points in the object and the image are the same distance away from a line. </li></ul><ul><li>You must specify one detail: the mirror line or line of symmetry. </li></ul><ul><li>A figure and its image are indirectly congruent (shape and size remain unchanged but the orientation changes) </li></ul>
  7. 7. Vectors A vector is an ordered pair of numbers that can be used to describe a translation. The notation is: Where a is the distance moved in the +X direction. And b is the distance moved in the +Y direction.

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