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12.4 Enlarging shapes

12.4 Enlarging shapes

When you enlarge a shape, all the lengths of the sides of the shape increase in the same proportion.
$is is called the scale factor. All the angles in the shape stay the same size.

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Worked example 12.4

a The diagram shows a trapezium. b The diagram shows two triangles A and B.
y
4 y
4
3
3
2
2
1 A
1
B
0 x
–4 –3 –2 –1 1 2 3 4 0 x
–1 –4 –3 –2 –1 1 2 3 4
–1
–2
–2
Draw an enlargement of the trapezium, with scale
factor 3 and centre of enlargement (−3, −2). Triangle B is an enlargement of triangle A.
Describe the enlargement.
a y First, mark the centre of enlargement at (−3, −2), shown as a red
4 dot on the diagram. The closest vertex of the trapezium is one
3 square up from the centre of enlargement.
2 On the enlarged trapezium this vertex will be three squares up
1 from the centre of enlargement (shown by the red arrows).
Mark this vertex on the diagram then complete the trapezium by
0 x drawing each side with length three times that of the original.
–4 –3 –2 –1 1 2 3 4
–1
–2

b y First, work out the scale factor of the enlargement.
4 Compare matching sides of the triangles, for example, the two
3 sides shown by the red arrows. In triangle A, the length is 2
2 squares and in triangle B the length is 4 squares.
A 4 ÷ 2 = 2, so the scale factor is 2.
1
B Now find the centre of enlargement by drawing lines (rays)
0 x through the matching vertices of the triangles, shown by the
–4 –3 –2 –1 1 2 3 4
–1 blue lines. The blue lines all meet at (4, 3).
–2 So, the enlargement has scale factor 2, centre (4, 3).

12 Tessellations, transformations and loci 119