Most of you should be able to …
Enlarge a shape on a centimetre grid (Grade E)
Enlarge a shape by a positive integer scale factor about a given centre of
enlargement (Grade D)
Find the “Centre of Enlargement”
Some of you should be able to …
Enlarge a shape by a positive fractional scale factor about a given centre of
enlargement (Grade C)
Starter The lantern throws a
shadow across the floor.
What would happen if the
lantern was closer to the
What would happen if it
was further away?
Starter Activity 2
What happens to the
shadow on the sundial
during the day?
Why does this happen?
Starter Activity 3
What are the coordinates?
6 (2, -3)
2 (-4, 3)-1)
–7 –6 –5 –4 –3 –2 –1
1 2 3 4 5 6 7 8 x
To enlarge a shape on a
centimetre grid, simply
multiply the lengths by
the scale factor.
Hint: You only need to
worry about the vertical
and horizontal lengths,
the diagonals will follow.
Scale Factor = 3
To enlarge a shape about a
centre of enlargement, draw
lines from the centre through
Scale Factor = 3
Now measure along the lines three times the original
distance from the centre of enlargement to each
vertex. This is where the corresponding vertex will
appear. Tip: You could use compasses.
The original vertices should labelled with normal letters.
The corresponding vertices on the image should be labelled
with dashed letters
Scale Factor = 2
What if the CoE is inside the shape?
Centre of Enlargement
What about if I need to find the centre of
9 found the
8 centre of
4 (2, 1)
0 1 2 3 4 5 6 7 8 9 x
These photographs are similar rectangles. What is the minimum amount of
information required to be able to fill in all of the missing lengths and multipliers?
Scale Factor = -1
• National Library
• Emaths (equivalent ratio Excel file)
Transformation – A change to a shape carried out under a specific rule (or set of rules)
Enlargement – a transformation in which lengths of an object are multiplied by the same amount to produce an image.
Scale Factor – this is the value of the multiplier used to enlarge an object. The multiplier for the area of an shape is the (Scale
Factor)2. The multiplier for the volume of an shape is (Scale Factor)3.
Centre of Enlargement – This is the point from which the enlargement is projected. Lines joining the corresponding vertices on the
Image and Original shapes will cross at the centre of enlargement.
Original (or object) – the shape that a transformation is carried out on. The shape that you start with. Usually labelled with
consecutive letters of the alphabet ABCD etc.
Image - when a transformation is carried out on an original shape, the shape which appears is called the image. Usually labelled
with dashed letters A’B’C’D’ etc, a second image would be labelled with double dashed letters A’’B’’ and so on.
Vertex (Pl. Vertices) – the corner of an object.
Axis (Pl. Axes) - for two-dimensional geometry there are two fixed axes, the x-axis and the y-axis. They cross at right angles and
allow positions to be defined by coordinates.
Coordinate – These give the position of a point by placing it in relation to some other fixed points, usually the numbers on a set of
axes. The x-axis coordinate is given first. For example, (2, 3) means the point which is two along the x-axis and three up the y-axis.
Origin – the point where the x-axis and y-axis cross. The coordinate (0, 0)
Similar – Shapes are said to be similar when they are the same in shape but different in size. One shape is an enlargement of the
other. Corresponding angles are the same size.
Congruent – Shapes are said to be congruent when they are exactly the same. Corresponding angles are the same size and
corresponding lengths are equal.
Ratio – This is used to compare the sizes of two (or more) quantities. For example, a drink is made by mixing two parts orange juice
with five parts water. This relationship of 2 to 5 can be written as the ratio 2:5.