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transformations An introduction to transformations is covered elsewhere at MathsNet Transformations. These pages look at more advanced aspects of transformation geometry .


A reflection has these properties:
  • For every straight line s there corresponds a reflection Ms. If A' is the image of A then A is the image of A'.
  • The points of s remain in the same position. They are the fixed points of Ms.
  • The reflection Ms preserves straight lines.
Easier
Reflection problem 1
Reflection problem 2
Reflection problem 3
Reflection problem 4		 Harder
Reflection problem 5


A rotation can be viewed as the product of two reflections whose mirror lines intersect at the point O. O is the centre of rotation.
Easier
Rotation problem 1		 Harder
Rotation problem 2
Rotation problem 3


A translation can be viewed as the product of two reflections whose mirror lines are parallel.
Easier
Translation problem 1		 Harder
Translation problem 2


Given a fixed point S, and a non-zero number m, an enlargement has these properties:
  • Every point A and its image A' lie on the same line through S.
  • Each pair A and A' satisfy the relation: SA'/SA = m
S is the centre and m is the scale factor of the enlargement.
  Harder
Enlargement problem 1
Enlargement problem 2
Enlargement problem 3


A spiral similarity is the product of a rotation and an enlargement with the same centre.
  Similarity problem 1