# Transformations in Shapes.

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- Created by: Rebecca Rubie
- Created on: 18-11-12 12:44

There are four different ways to change the appearance of a shape:

- Translation
- Reflection
- Rotation
- Enlargement

TRANSLATION:

If we **translate** an object, we move it up or down or from side to side. But we **do not** change its shape, size or direction.

**For example:**

Q **is** a translation of triangle ABC. Triangle ABC has been translated 3 squares to the right and 2 squares up.

P **is not** a translation of triangle ABC because the object and its image are facing in opposite directions.

R **is not** a translation of triangle ABC because the object and its image have different side lengths. They are different shapes.

**When we translate an object, every vertex (corner) must be moved in the same way.**

Triangle PQR has been translated 3 squares down and 4 squares to the right. All of the vertices have been translated in the same way, and the object and its image are exactly the same shape and size.

# Using vectors to describe translations:

The line **AB** has been translated 4 units to the right and 2 units upwards. We say that the displacement vector is

**We always write the horizontal displacement at the top of the vector and the vertical displacement at the bottom.**

**A move downwards or to the left is indicated by a - sign:**

Model Question and Answer:

**P'** (7, 2) is the image of **P** (2, 11) after a translation. What vector describes this translation?

**To work out the horizontal movement after the translation, subtract the x-coordinates for p from p':**

**7 - 2 = 5**

**To work out the vertical movement after the translation, subtract the y-coordinates for p from p':**

2 - 11 = - 9

**The vector that describes the translation is:**

If you are not sure…

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