Enlargements (Edexcel IGCSE Maths)

Start by marking on the centre of enlargement (CoE).
Count the number of squares in both a horizontal and vertical direction to go from the CoE to one of the vertices on the original object, this is 2 to the right and 3 up in this example.
As the scale factor is 2, multiply these distances by 2, so they become 4 to the right and 6 up.
Count these new distances from the CoE to the corresponding point on the enlarged image and mark it on.
Draw a line through the CoE and the pair of corresponding points, they should line up in a straight line. 

Repeat this process for each of the vertices on the original object.
Join adjacent vertices on the enlarged image as you go.
Label the enlarged image C'.

Because the scale factor is 2, each of the lengths will be twice as long on the enlarged image as they are on the original object.
Square the length scale factor to find the area scale factor.

The length scale factor is 2, therefore the area scale factor will be 2² = 4, hence, the area of C' is 4 times larger than C

You can see that the image is larger than the original object, therefore it must be an enlargement.
As the enlarged image is bigger than the original object, the scale factor must be greater than 1.
Compare two corresponding edges on the object and the image to find the scale factor.

The height of the original "H" is 3 squares, the height of the enlarged "H" is 9 squares.

Draw a straight line through the CoE and a pair of corresponding points on the original object and the enlarged image.
Repeat this step for all of the pairs of vertices on the object and image.
The point of intersection of the lines is the CoE.

Shape A has been enlarged using a scale factor of 3 and a centre of enlargement (9, 9) to create shape B