April 13, 2023

Transformations

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1. Reflections, rotations and translations.

April 13, 2023

Here is a large mirror.If we place an object in front of it, we see a mirror image.

Now imagine we could look at both the real image and the reflection from overhead. Notice that any point on the real object is the same distance from the plane of the mirror in its reflection.

Explanation

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April 13, 2023

MirrorReal object

Reflection

Each point on the real object has a corresponding point the same distance from the mirror.

A line joining corresponding points will always pass through the mirror at right-angles to it.

Explanation

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April 13, 2023

You can produce accurate reflections on squared paper.

“Reflect the shape DEFG in the line WX.”

Look at each point in turn.

D E

F

G

A line from D, that meets the mirror at right angles, needs to be two diagonal squares long. The image of D is therefore two diagonal squares beyond the mirror along the same line.

A line from E, that meets the mirror at right angles, needs to be one and a half diagonal squares long. The image of E is therefore one and a half diagonal squares beyond the mirror along the same line.

A line from F, that meets the mirror at right angles, needs to be two and a half diagonal squares long. The image F is therefore two and a half diagonal squares beyond the mirror along the same line.

A line from G, that meets the mirror at right angles, needs to be one and a half diagonal squares long. The image of G is therefore one and a half diagonal squares beyond the mirror along the same line.

You may like to label each point as you go along, to help you join them up correctly.Remember, you are creating a mirror image of the original, so it should look back to front.

D

E

FG

Despite being a mirror image, The original shape and its reflection are still congruent.

W

X

Explanation

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April 13, 2023

Here is the flag shape again.

This transformation is called a rotation.To rotate a shape, you need to know…The angle of rotationThe direction of rotationThe centre of rotation

180ºanticlockwise(-2,1)

y

-1

-2

-3

-4

1

234

x0-1-2-3-4 1 2 3 4

Explanation

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April 13, 2023

Remove the tracing paper and join up the marks you have made.Unless otherwise stated, all rotations should be anticlockwise.Make sure that your tracing paper covers both the shape and the centre of rotation.Use your pencil to keep the tracing paper fixed at the centre of rotation, whilst you rotate it 270º.Use the point of your pencil to mark the rotated position of the corners of the shape, through the tracing paper.Carefully trace the shape.

D E

F

The easiest way to perform a rotation is with tracing paper.

0

“Rotate shape DEF 270º anticlockwise, around point 0”

You can also perform a rotation by counting squares, or by using a pair of compasses.With the point of the compasses on the centre of rotation, draw an arc 270º for each point.

Explanation

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April 13, 2023

This transformation is called a translation.

Each point on the shape has moved the same distance, in the same direction.You need to describe how many squares up, or down and how many squares left or right it has moved.Use a single point to work this out.Both shapes are congruent.

Two squares down.

Three squares right.

Explanation

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