# Chapter 15: Transformation and Similarity

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## 15.1 Reflections

Some objects possess mirror symmetry, or reflection symmetry.

2D objects have a mirror line, dividing the object into two matching (congruent: the same shape and size) halves, one a mirror image of the other.

3D images have a plane of symmetry

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## 15.2 Rotations

These are objects that are turned to face in a different direction while remaining the same shape and size. The pivot for the rotation is the centre of rotation. In order to answer a rotation question, include:

• Angle of rotation
• Clockwise/anticlockwise
• Centre of rotation

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## 15.3 Combining Transformations

Reflection, rotation and translation preserve congruence. Translations consist of sliding an object up, down, left or right. You write this in a column vector:

This would be B, because the shape moves 5 units right and 2 units down.
Sometimes, you will have to combine transformations to 'map' one object onto another

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## 15.4 Enlargements

When enlarging, you must specify a centre of enlargement and a scale factor. It often helps to draw rays from the centre of enlargement

• Scale factor greater than 1: simple enlargement- object gets bigger
• Scale factor between 0 and 1: the enlargement is a reduction- object gets smaller
• Negative scale factor: object is enlarged/reduced and inverted

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## 15.5 Similar shapes and solids

Similarity: objects are the same shape but one is an enlargement of the other. If the enlargement factor is n:

• Corresponding lengths are in the ratio 1:n
• Corresponding areas are in the ratio 1:n(squared)
• Corresponding volumes are in the ratio 1:n(cubed)

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