Page 121 - Cambridge+Checkpoint+Mathematics+Coursebook+9

12.4 Enlarging shapes

) Exercise 12.4

y
1 The diagram shows a triangle on a coordinate grid.
3
Make a copy of the diagram on squared paper. 2
On the copy, draw an enlargement of the triangle with 1
scale factor 3, centre (−2, 0).
0 x
–4 –3 –2 –1 1 2 3 4
–1
2 The diagram shows a shape on a coordinate grid. y
4
Make three copies of the diagram on squared paper. 3

a On the first copy, draw an enlargement of the shape with
2
scale factor 2, centre (2, 2).
1
b On the second copy, draw an enlargement of the shape with
scale factor 3, centre (3, 3). –4 –3 –2 –1 –1 0 1 2 3 4 x
c On the third copy, draw an enlargement of the shape with –2
scale factor 2, centre (3, 4). –3

–4
3 The diagram shows three triangles, A, B and C, on y
6
a coordinate grid.
5
a Triangle B is an enlargement of triangle A.
Describe the enlargement. 4
3
b Triangle C is an enlargement of triangle A. C
Describe the enlargement. 2
1
4 The vertices of rectangle X are at (1, −2), (1, −3), (3, −3) 0 x
–6 –5 A –4 –3 –2 –1 1 2 3 4 5 6
and (3, −2). –1
The vertices of rectangle Y are at (−5, 4), (−5, 1), (1, 1) –2
and (1, 4). B –3
Rectangle Y is an enlargement of rectangle X. Describe –4
–5
the enlargement.
5 Sasha drew a triangle with vertices at (1, 1), (2, 1) and (1, 3).
She enlarged the shape by a scale factor of 3, centre (0, 0). Read what Sasha said.

If I multiply the coordinates of each vertex by 3 it will give me the
coordinates of the enlarged triangle, which are at (3, 3), (6, 3) and (3, 9).

a Show, by drawing, that in this case Sasha is correct.
Read what Ahmad said.

This means that, for any enlargement, with any scale factor and centre
of enlargement, I can multiply the coordinates of each vertex by the
scale factor to work out the coordinates of the enlarged shape.

b Use a counter-example to show that Remember that a counter-example is just one
Ahmad is wrong. example that shows a statement is not true.

120 12 Tessellations, transformations and loci