Ideas for Extension 
The following ideas for extending this topic require the full version of Autograph. 

Idea 1 – Introducing Enlargements 
Download 1. Introducing Enlargements.agg 


You can use Autograph to introduce students to the very basics of enlargement, and use the same process to take them right up to fractional and negative scale factors. 

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Challenge your students to predict and Scribble down where they think the image will appear following an enlargement of scale factor 2 with centre at the circled point 
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When they are ready click on the object and the centre of the point, rightclick and choose Enlargement 
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Choose the scale factor 
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Decide if you want to show construction lines and then click OK 
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Ask the students to predict what happens if you increase the scale factor 
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Use the Animation Controller to dynamically change the scale factor 
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Now what happens when the scale factor goes below 1? 
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How about when it is negative? 
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Use the Animation Controller to illustrate this, emphasising the smooth progression as the scale factor decreases in size 

Idea 2 – Finding the Centre of Enlargement 
Download 2. Find the Centre.agg 


This file provides a clear illustration of how to find the centre of an enlargement 

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Challenge your students to predict where they think the centre of enlargement is and Scribble down a prediction 
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Choose one of the dashed lines to start with 
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Drag the circled points to a pair of corresponding corners on the original object and the enlarged image 
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Repeat this for the other three remaining lines until each corner of the two objects has a line passing through them 
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Where these lines meet is the centre of enlargement 
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To set up another example, go to Object > Unhide all, drag the centre of enlargement (and the corners of the object, if you choose) to a new position, then select the point, rightclick and choose Hide Object 
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Doubleclicking on the enlarged image allows you to change the scale factor, should you wish 

Idea 3 – Area Scale Factor 
Download 3. Area Scale Factor.agg 


Enlargements are an ideal way to look at area scale factor 

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Challenge your students to predict what will happen to the area of the rectangle if you enlarge it with scale factor 2 
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Carry out the enlargement as described in Idea 1 
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Can they explain this answer? 
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Can they now predict the area if the scale factor is 3? 
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How about scale factor ½? 
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Drag the corners of the shape around and change the centre of enlargement to challenge your students further 

Idea 4 – Enlargements in 3D! 
Download 4. Enlargements in 3D.agg 


You can also use Autograph’s unique 3D engine to investigate enlargements in three dimensions, and volume scale factors 

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Challenge your students to predict the coordinates of the image of the cube following an enlargement of scale factor 2 from centre (0, 0, 0). 
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How about the volume of the new image? 
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Enlargements in 3D work exactly the same as enlargements in 2D, so just select the point and the cube, rightclick, choose your scale factor and click OK. 
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Can your students explain what has happened? 
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Change the centre of enlargement, the enlargement scale factor, or the shape itself to further challenge your students 
