Transformations in Shapes.

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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.

image: a graph with 4 triangles plotted (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/graph_62.gif)

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.

image: a graph with 2 triangles plotted (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/graph_63.gif) 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 4 over 2 (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/transformationsrev3_1.png)

image: a graph with two lines plotted, the first at 1,1 and 2,4 the second at 5,3 and 6,6 (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/graph_64.gif)

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:5 over -9 (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/transformationsrev3_3.png)

If you are not sure…

Comments

daviesg


A really good set of revision notes on transformations

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