GEOMETRY(iv)

Contents:

 

Transformations: There are four transformations mentioned:

Translation, Enlargement, Rotation, and Reflection.

Translation: The shifting of all points in a fixed direction.

Need: (1). Grid reference 'x' and 'y'.

Triangle ABC to -8, 5.

Look at any point on the triangle, eg. A.

Triangle ABC point A is placed at position 4 on the 'x' axis and at position -1 on the 'y' axis. If translated -8 on the 'x' axis and +5 on the 'y' axis it appears as:

Triangle ABC where point A is placed at position -4 on the 'x' axis, and at position 4 on the 'y' axis.

The translation is -8, 5. (The 'x' axis is always shown first).


Enlargement: Increases the size and shape by a constant factor.

Need: (1). Scale Factor, and (2). Centre of Enlargement using Grid Ref.

Triangle ABC Scale Factor 2, Centre ,.

Lines A to A, B to B, C to C meet at position on the 'x' axis, and at position on the 'y' axis.

The length of the lines are 1 : 2. which is the Scale Factor.

 

 

 


Rotation: Turns all points through a fixed angle.

Need: (1). Angle and (2). Direction and (3). Centre of Rotation.

Triangle ABC 90, Clockwise, A.

The centre of rotation is point A, turn the triangle by 90 from the point, to Triangle ABC.

 

 

 


Reflection: Moves each point to its mirror image on the other side of a fixed line.

Need: (1). The line of reflection.

The line of reflection is 'x' = 'y'.

Triangle ABC is reflected over the line.

Point A = -1, 3 reflected to: A = 3, -1.

Point B = -5, 3 reflected to: B = 3, -5.

Point C = -3, 1 reflected to: C = 1, -3.

 

 


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