| Ideas for Extension |
| The following ideas for extending this topic require the full version of Autograph. |
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| Idea 1 – Introducing Enlargements |
Download  1. Introducing Enlargements.agg |
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| 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 | | • | When they are ready click on the object and the centre of the point, right-click and choose Enlargement | | • | Choose the scale factor | | • | Decide if you want to show construction lines and then click OK | | • | Ask the students to predict what happens if you increase the scale factor | | • | Use the Animation Controller to dynamically change the scale factor | | • | Now what happens when the scale factor goes below 1? | | • | How about when it is negative? | | • | Use the Animation Controller to illustrate this, emphasising the smooth progression as the scale factor decreases in size |
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| Idea 2 – Finding the Centre of Enlargement |
| Download 2. Find the Centre.agg |
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| 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 | | • | Choose one of the dashed lines to start with | | • | Drag the circled points to a pair of corresponding corners on the original object and the enlarged image | | • | Repeat this for the other three remaining lines until each corner of the two objects has a line passing through them | | • | Where these lines meet is the centre of enlargement | | • | 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, right-click and choose Hide Object | | • | Double-clicking on the enlarged image allows you to change the scale factor, should you wish |
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| Idea 3 – Area Scale Factor |
| Download 3. Area Scale Factor.agg |
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| 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 | | • | Carry out the enlargement as described in Idea 1 | | • | Can they explain this answer? | | • | Can they now predict the area if the scale factor is 3? | | • | How about scale factor ½? | | • | Drag the corners of the shape around and change the centre of enlargement to challenge your students further |
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| Idea 4 – Enlargements in 3D! |
| Download 4. Enlargements in 3D.agg |
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| 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 co-ordinates of the image of the cube following an enlargement of scale factor 2 from centre (0, 0, 0). | | • | How about the volume of the new image? | | • | Enlargements in 3D work exactly the same as enlargements in 2D, so just select the point and the cube, right-click, choose your scale factor and click OK. | | • | Can your students explain what has happened? | | • | Change the centre of enlargement, the enlargement scale factor, or the shape itself to further challenge your students |
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Scribble down where they think the image will appear following an enlargement of scale factor 2 with centre at the circled point
click on the object and the centre of the point, right-click and choose Enlargement
Animation Controller to dynamically change the scale factor
