Enlargements Objectives To be able to Enlarge shapes

Enlargements Objectives To be able to: Enlarge shapes given a scale factor and centre of enlargement. Find centres of enlargement

Scale factors and centres of enlargement The size of an enlargement is described by its scale factor. For example, a scale factor of 2 means that the new shape is twice the size of the original. The position of the enlarged shape depends on the centre of enlargement.

Enlarge triangle A with a scale factor of 3 and centre of enlargement (2, 1) Draw lines from the centre of enlargement to each vertex of your shape y 10 9 8 7 6 5 4 3 2 1 Calculate the distance from the Co. E to a vertex and multiply it by the scale factor to find its new position How do I enlarge a shape? A’ Repeat for all the other vertices Join up your new points to create your enlarged shape A 0 1 2 3 4 5 6 7 8 9 10 x

y 9 8 7 6 5 4 3 2 1 What if the centre of enlargement is inside the shape? Enlarge shape B with scale factor 2 and centre of enlargement (6, 6) B B’ 0 1 2 3 4 5 6 7 8 9 10 x

Enlarge shape C by scale factor ½ and centre of enlargement (10, 1) What about fractional scale y factors? 9 8 7 6 5 4 3 2 1 Each vertex on the enlarged shape is half the distance from the Co. E than its corresponding vertex on the original shape. 0 1 2 3 4 5 6 7 8 9 10 Even though the shape gets smaller, it’s still called an x enlargement.

How do I find the centre of enlargement? y 10 9 8 7 6 5 4 3 2 1 Join up the corresponding vertices and extend the lines The point where they all intersect is your centre of enlargement E Co. E = (2, 9) D 0 1 2 3 4 5 6 7 8 9 10 x What was the scale factor of enlargement?