Enlargement

Triangle 1 has a length of 8 and a height of 5. If we were to increase the size of Triangle 1 by a scale factor of 2 it would double these dimensions to give us Triangle 2 which has length 16 and a height of 10. This is the basic idea of enlargement.
 * __Scale Factor Enlargement__**



We can do the same thing using a grid. In picture (A) the quadrilateral OZYX has been enlarged by a scale factor of 2.5 to form the quadrilateral OZ1Y1X1. We can identify this by comparing the co-ordinates of Y(2,1) and Y1(5,2.5). As the x co-ordinate of Y is 2 enlarging by a scale factor of 2.5 will give the new x co-ordinate of 5. If we do the same thing with the y co-ordinate, it changes from 1 in Y to 2.5 in Y1. This also holds true for the co-ordinates being enlarged from X to X1 and Z to Z1.
 * __Scale Factor Enlargement on a Grid__**



Using the same shape as above it can be shown how a fractional scale factor effectively reduces the size of the shape by that scale factor. Quadralteral OABC has been enlarged by a scale factor of 1/3 to produce quadrilateral OA1B1C1. This is clarified by taking point C which has a co-ordinate of (0,6) and enlarging by a scale factor of 1/3 gives C1 the co-ordinate of (0,2). Again this applies in the tranformations of A to A1 and B to B1. Even though still classed as enlargement, any enlargement by a fractional scale factor makes transformed shape smaller than the original shape.
 * __Fractional Scale Factors__**