Transformations

Transformation involves moving an object from its original position to a new position.  The object in the new position is called the image. Each point in the object is mapped to another point in the image.  The three main Transformations are: Rotation Turn! Reflection Flip! Translation Slide! After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths. If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called Congruent. Resizing The other important Transformation is Resizing (Dilation) (also called dilation, contraction, compression, enlargement or even expansion). The shape becomes bigger or smaller: Resizing If you have to Resize to make one shape become another then the shapes are not Congruent, but they are Similar. Congruent or Similar So, if one shape can become another using transformation, the two shapes might be Congruent or just Similar If you ... Then the shapes are ... ... only Rotate, Reflect and/or Translate  Congruent ... need to Resize Similar http://www.mathsisfun.com/geometry/transformations.html Rotation "Rotation" means turning around a center: The distance from the center to any point on the shape stays the same. Every point makes a circle around the center. Here a triangle is rotated around the point marked with a "+" Reflection Video on Reflection Transfermation (Click here) the reflected image is always the same size, it just faces the other way: A reflection is a flip over a line How Do I Do It Myself? Just approach it step-by-step. For each corner of the shape: 1. Measure from the point to the mirror line (must hit the mirror line at a right angle) 2. Measure the same distance again on the other side and place a dot. 3. Then connect the new dots up! Labels It is common to label each corner with letters, and to use a little dash (called a Prime) to mark each corner of the reflected image. Here the original is ABC and the reflected image is A'B'C' Some Tricks X-Axis If the mirror line is the x-axis, just change each (x,y) into (x,-y) Y-Axis If the mirror line is the y-axis, just change each (x,y) into (-x,y) Fold the Paper And if all else fails, just fold your sheet of paper along the mirror line and then hold it up to the light ! Reflection Symmetry Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to recognise, because one half is the reflection of the other half.
Rotational Symmetry With Rotational Symmetry, the shape or image can be rotated and it still looks the same. How many matches there are as you go once around is called the Order. If you think of propeller blades (like below) it makes it easier. Examples of Different Rotational Symmetry Order Order Example Shape Artwork (using Symmetry Artist) ... and there is also Order 5, 6, 7, and ... ... and then there is Order 9, 10, and so on ... Is there Rotational Symmetry of Order 1 ? Not really! If a shape only matches itself once as you go around (ie it matches itself after one full rotation) there is really no symmetry at all, because the word "Symmetry" comes from syn- together and metron measure, and there can't be "together" if there is just one thing.   W          Real World Examples A Dartboard has Rotational Symmetry of Order 10 The US Bronze Star Medal has Order 5 The London Eye has Order ... oops, I lost count!