Here we will learn about the centre of enlargement, including how to enlarge a shape about a point. We will also learn about fractional scale factors and negative scale factors.
There are also enlargement worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
Centre of enlargement is a point which tells you where to draw an enlargement.
An enlargement is a type of transformation where we change the size of the original shape to make it bigger or smaller by multiplying it by a scale factor.
To use a centre of enlargement we need to draw lines from the centre of enlargement through the vertices of the original shape. These are called ray lines.
Here triangle ABC has been enlarged by scale factor 2 about a centre of enlargement point O.
The new triangle is labelled A’B’C’.
The lengths of the sides of the new shape are double the lengths of the sides of the original shape. The pairs of corresponding sides are parallel lines. The angles in the two shapes are the same and the triangles are similar triangles.
Here triangle ABC has been enlarged by scale factor \frac about a centre of enlargement point O. If an enlargement is between 0 and 1 the shape becomes smaller. The new triangle is labelled A’B’C’.
The lengths of the sides of the new shape are a third of the lengths of the sides of the original shape.
The pairs of corresponding sides are parallel lines.
The angles in the two shapes are the same and the triangles are similar triangles.
A transformation, such as an enlargement, is a type of mathematical mapping. So the term “maps” is often used in questions.
A mapping is a mathematical instruction and a transformation is a mathematical instruction which can be applied to a shape.