Geometry and Transformations

Geometry and Transformations

1. Enlargement [clip 76]

   • Enlargement with a point of enlargement
     • This means that the enlargement has to be the right size and in the right position
     • Example: scale factor 2
     • Draw a guideline from the centre of enlargement through one of the points of the shape
       • Count how to get from the centre to the point then multiply this by the scale factor
         • E.g centre to Point A is Across 1 Up 5
           • For the enlargement this needs to be done twice, so the new position of A is Across 2 Up 10 from the centre of enlargment
         • From the new position the rest of the sides can be worked out as before, by multiplying them by the scale factor
   • Multiply each side by the scale factor
     • E.g Scale factor-2 ................ side x 2
       • B is the enlargement of A by the scale factor 2
       • This is increases the size of the shape
     • E.g Scale factor 1/2 ................ side x 1/2 (0.5)
       • C is the enlargement of A by scale factor 1/2
       • Multiplying by 1/2 is the same has dividing by 2. So the size of the shape is decreased
     • When there is no point of enlargement, the enlarged shape can go anywhere

2. Enlargement by a negative scale factor [clip 171]

   • Mark out the centre of enlargement
     • Draw guidelines from the orginial shape through the centre and carry them on
       • Count how to get from the centre to the point then multiply this by the scale factor
   • Example: the scale factor is -2 and the centre of enlargement is (1,0)
     • Because the scale factor is a negative the new shape is on the opposite side of the centre of enlargement than the original shape

3. Describing an enlargement

   • 1. name the translation 2. work out scale factor 3. find centre of enlargement
     • if the shapes are different sizes then it is an enlargement.
     • Divide the length of a side from the enlarged shape by the length of a side on the original shape to work out scale factor
     • To find the centre of enlargement join two like points with a line and carry it on. Do this for 2 or more points.
       • Where the lines cross is the centre of enlargemrnt

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