Enlargement

Key Facts and Exam Tips

• If a shape is enlarged, the image produced will be mathematically similar to the original shape. All lengths in all dimensions are multiplied by the same amount, producing an image that has the same proportions as the original.
  
• Lengths in the image may be larger or smaller than in the original but all angles will remain the same, so retaining the essential shape of the object.
  
• The scale factor of enlargement is the number that all the original lengths are multiplied by to produce the image.
  
• The scale factor can be calculated by measuring a pair of corresponding sides in the original shape and in the image and calculating the ratio enlarged length/original length.
  
• You can check your calculation by choosing a different pair of corresponding sides and finding their ratio - it should be the same.
  
• If you are given the centre of enlargement you need to draw lines from this point to each corner (vertex) of your shape. Now measure the distance from the centre to each corner. Multiply each distance by the scale factor given and this tells you how far from the centre each corner in the image needs to be. For each corner measure and mark this distance along the lines you have drawn, extending the lines if necessary (with a ruler!). Finally, join the corners of the image to produce the required shape. Check that it looks 'similar' to the original.
  
• Always measure from the centre of enlargement not from the corners.
  
• If you are working on a squared grid you can also count squares horizontally and vertically from the centre of enlargement to each corner. Multiply by the scale factor and count the number of squares horizontally and vertically, from the centre, to get the position for each corner in the image.
  
• You can reverse this process if you are asked to find the centre of enlargement. Simply draw lines through corresponding corners in the original image and extend them back until they meet. The point where they meet is the centre. Only two lines are strictly needed but you should draw a third line to act as a check.
  
• Work with a sharp pencil and leave all construction lines visible so that you gain maximum marks for method.
  
• Scale factors greater than 1 produce a bigger image further from the centre. Fractional scale factors, between 1 and 0, produce a smaller image nearer to the centre.
  
• Choosing a different centre of enlargement will alter the position of the final image.