1. List three examples of transformations.

2. Is enlargement a transformation?

3. Find the image of the point B(−3, 6) after a reflection in the x-axis.

4. Find the image of the point D(2, −5) after a reflection in the y-axis.

5. Find the image of the point Q(6, −8) after a rotation through 90° about the origin in the anticlockwise direction.

6. Find the image of the point N(−2, 3) after a rotation through 270° clockwise about the origin.

7. Find the image of the point (6, 2) after a rotation of 180° about the origin in the anticlockwise direction.

8. A translation takes the origin to (−6, 1), find where it takes (2, −5).

9. A translation takes the points (0, 6) to (0, 10). Where does it take (2, −3)?

10. Draw a parallelogram ABCD with vertices A(2, 5), B(5, 5), C(6, 8) and D(3, 8). Draw the image of the parallelogram ABCD formed by reflection in the y–axis.

11. If ΔPQR ~ ΔLMN such that ∠MLN = 40° and ∠QRP = 60°, find:
(a) ∠PQR    (b) ∠QRP + ∠RQP.

12. On the map of a certain place, a line segment joining two points is 5 cm long. The distance between the actual points represented is 125 km, find the scale of the map.

13. The length and width of a rectangular field on a map of a certain town are 10 cm and 8 cm, respectively. If the scale of the map is 1:400,000, find:
(a) the actual length of the field.
(b) the actual width of the field.
(c) the area of the field in square metres.

14. If two polygons are similar and the ratio of their corresponding sides is 5:3, what is the enlargement factor?

15. A ladder 5 metres long leans against a vertical wall. The point at which the ladder meets the ground is 3 metres from the wall. Use a scale drawing to find how high up the wall the ladder touches the wall.

16. Use the following figure to find the enlargement factor of ΔABC and the scale factor of its area, and hence find its area given that the area of ΔPBA is 10 cm².