Enlargements Objectives To be able to:

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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.

How do I enlarge a shape? A’ y 10 9 8 7 6 5 4 3 A 2 1 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 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y 10 Calculate the distance from the CoE 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 A Join up your new points to create your enlarged shape

What if the centre of enlargement is inside the shape? 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y 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

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

How do I find the centre of enlargement? 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y 10 Join up the corresponding vertices and extend the lines The point where they all intersect is your centre of enlargement E D CoE = (2,9) Scale factor could be 2 or ½ depending on which way they enlarge the shapes What was the scale factor of enlargement?