Enlarging and Reducing geometric figures
We've studied the 3 types of transformations, translation, rotation and reflection and we know that these shapes does not change in size or shape. These transformations can also be called congruent shapes(shapes with the same size and shape), because the object and the image have the same shape and same size.
Enlargement and reductions
Enlargement is the transformation of an object that has the same shape, but increases in size of the object.
Enlargement of a triangle by a scale factor 3
In the above example we can see that triangle PQR is enlarged by a scale factor of 3 to give triangle P'Q'R'
Scale factor is how many times the object has enlarged.
Scale factor of 3 means that the object (original) triangle was trippled to give the image (enlargement).
Reduction:
Reduction is a transformation of an object that has the same shape, but decreases in size of the object.
Reduction of a shape by a scale factor of 2
In the above example, we can see that the shape has been reduced by a scale factor of 2. Each of the sides are half of the original shape.
We can say that the scale factor is a half. (Factor of reduction)
In both enlargement and reduction, the angles of the shapes remain the same, only the sides of the shape enlarge (bigger) or reduce (smaller).
Enlargement and reduction is an example of similar shapes (shapes with the same shape but different sizes).
The amount of which the object is enlarged or reduced is called the factor of enlargement or the factor of reduction. This can also be called the scale factor, we just have to indicate if the object is an enlargement or reduction.
When changing the size of object by enlargement or reduction, we enlarge or reduce the sides of the object from a point called the centre of enlargement or the centre of reduction.
This transformation is not rigid, the size of the shape changes. Think of looking at a flower through a magnifying glass. You still see a flower, but the size of the flower will be bigger.
Factor of enlargement around the centre point with a scale factor of 2
Note that the centre of enlargement is at (0,0), if the object (original) shape is 1 block away from the centre point, the image will be 2 blocks away, the base of the image is 1 block to the right, so the image will be 2 blocks to the right etc.
Activity for enlargement and reduction:
