Transformations and Vectors 1

Transformations and Vectors 1

Learning Objectives

• Reflect, rotate, translate and enlarge plane shapes

• Use vectors to describe translations

  Calculate the magnitude of a vector Represent vectors in conventional ways

  Use the sum and difference of vectors to express them in terms of coplanar vectors

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Transformations (1)

• Transformations that change the position of an object but do not alter its shape or size. 

• After these transformations an object and its image are congruent.

Transformations (2)

• Enlargement changes the position and size of an object, but not its shape. 

• After an enlargement the object and its image are similar.

Reflections

• Reflection flips a shape over a mirror line.

• The object and the image are the same distance from the mirror line. 

Example

• Other lines eg the line y = x or the line x = 1 can be used as the mirror line.

Rotations

• A rotation is a turn about a fixed point.

• A rotation can be either clockwise  or anticlockwise .

Translations

• A translation on a coordinate grid can be described using a column vector.

• The original shape and its image after translation are congruent to each other.

​Describing movements

Enlargement

• ​The scale factor for the enlargement

• The centre of enlargement

Negative scale factor

• A negative scale factor, moves the object to the opposite side of the centre of enlargement. 

• The distance of each vertex from the centre of enlargement is multiplied by the scale factor.

Vectors

Vectors

Vectors

Vectors

Vectors