Transformations

A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the object and the final shape and position of the object is the image under the transformation. Types of transformations in math • • • •

Translation Reflection Rotation Dilation

A combined transformations means that two or more transformations will be performed on one object. For instance, we could perform a reflection and then a translation on the same point.

Turn! "Rotation" means turning around a center: The distance from the center to any point on the shape stays the same.

Flip! Reflection is basically a 'flip' of a shape over the line of reflection. Every point is the same distance from the central line (line of reflection) ! ... and ... The image has the same size as the original object. The orientation of the image is laterally inverted, that is they are facing opposite directions. Example :

For any rotation, we need to specify the centre, the angle and the direction of rotation In the diagram, the figure A is reflected in the line XY. Note that the point O remained unchanged under reflection because it is on the axis of reflection. Any point on the line of reflection is unchanged – such points are described as invariant.

Example

Slide! In Geometry, "Translation" simply means Moving Every point of the shape must move: • •

the same distance in the same direction.

Translations: Interactive Activity

After any of those transformations (turn, flip or If one shape can become another using Turns, Flips slide), the shape still has the same size, area, and/or Slides, then the two shapes are called angles and line lengths. Congruent An enlargement is a transformation that produces an image that is the same shape as the original, but is a different size. Enlargement is a transformation in which each point of an object is moved along a straight line. The straight line is drawn from a fixed point called the centre of enlargement. The distance the points move depends on the scale factor. Resize! Enlargement. The shape becomes bigger or smaller. To resize, just do this for every corner: • • •

In enlargement, the centre of enlargement is the only invariant point. Scale factor =

draw a line from the central point to the corner increase (or decrease) the length of that If the scale factor is greater than 1, the image is an line enlargement. put a dot at the new point

Then just connect the dots for the resized shape!

If the scale factor is between 0 and 1, the image is a reduction