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End-of-unit review

End-of-unit review

1 Explain why a regular pentagon will not tessellate.
Show all your working and include diagrams in your explanation.
2 The diagram shows triangle A on a coordinate grid. y
Make a copy of the grid. 6
a Draw the image of triangle A after a reflection in the 5
line x = 4. Label the image B. 4
b Draw the image of triangle A after a translation described 3
−  1  2
by column vector   . Label the image C. A
 3  1
0
c Draw the image of triangle A after a reflection in the 0 1 2 3 4 5 6 7 x
line y = 4 followed by a rotation 180° about the point (3, 5).
Label the image D.
3 The diagram shows triangles A, B, C, D, E and F o a coordinate grid. y
Describe the single transformation that transforms: 4
a triangle A to triangle B 3 D
b triangle C to triangle D E 2 1
c triangle E to triangle F A
d triangle A to triangle E –4 –3 –2 –1 0 1 2 3 4 x
e triangle C to triangle E. –1 F
–2
B
–3 C
–4

4 The diagram shows a shape on a coordinate grid. y
Make two copies of the diagram, on squared paper. 4
a On the first copy, draw an enlargement of the shape with 3
scale factor 2, centre (0, 0). 2
b On the second copy, draw an enlargement of the shape 1
with scale factor 3, centre (3, −2). –6 –5 –4 –3 –2 –1 0 1 2 3 4 x
–1
–2
–3
–4

5 The vertices of triangle G are at (3, 2), (5, 2), and (5, 3).
The vertices of triangle H are at (7, 2), (13, 2), and (13, 5).
Triangle H is an enlargement of triangle G.
Describe the enlargement.

6 On a piece of plain paper, mark a point Q.
Draw the locus of points that are exactly 4 cm from point Q.

7 Draw a line segment XY, 8 cm long. X Y
Draw the locus of points that are exactly 2 cm from XY. 8 cm

12 Tessellations, transformations and loci 123