Enlargements (OCR GCSE 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

On the grid below enlarge shape F using scale factor    and centre of enlargement  . 

Label this shape F'.

If the area of F is 45 cm² write down the area of F'.

Start by marking the centre of enlargement (CoE) (6, -1) and selecting a starting vertex.

Count the horizontal and vertical distances from the vertex to the CoE.
Multiply those distances by the scale factor.

Vertex at (-4, 3)

Distance to CoE from vertex on original object: 3 to the right and 3 up

Distances from CoE to corresponding vertex on enlarged image: to the right and  up

Counting the new distances from the CoE, on the other side from the original object, mark on the position of the corresponding point on the enlarged image.
Draw a straight line through the corresponding vertices and the CoE to check that they line up

Repeat this process for each vertex in turn.

Connect the vertices as you go around so that you don't forget which should connect to which.

Remember, your enlarged image will be rotated by 180^o.

The length scale factor is  , meaning that each edge of the enlarged image is  the length of the corresponding edge on the original object.

Find the area scale factor by squaring the length scale factor.

Multiply the area of the original object by the area scale factor to find the area of the enlarged image.