1. Transformations

2. Reflections Lines of symmetry do not always have to touch the object
Image
Mirror line

3. Object
Image
Mirror line

4. Copy these axes on to squared paper
Plot these points
A(1, 2), B(2, 4) C(5, 1) A2 B2 C2 B
Join the points to get triangle ABC A C
Reflect triangle ABC in the x-axis to get a new triangle A1B1C1 A1 B1 C1 A3 B3 C3
Reflect triangle ABC in the y-axis to get a new triangle A2B2C2
Reflect triangle ABC in the y = -x to get a new triangle A3B3C3

5. Translations A translation can be thought as a sliding movement
Translate the triangle 4 squares to the right
4 squares

6. Translate the triangle 3 squares upwards

7. Translate the triangle 4 squares to the right and 3 squares upwards
This is written as
Movement right or left
3 squares
Translation
4 squares
Movement up or down

8. For translating the triangle 4 squares to the right and 3 squares upwards the movement can be thought as like this
Translation

9. For translating the triangle 3 squares to the
left and 4 squares downwards the movement
can be thought as like this
This is written as
Translation

10. Rotations
In a rotation an object is turned about a point through an angle. The point is called the centre of rotation.
Anticlockwise rotations are positive and clockwise are negative
Rotate triangle ABC about O through to get a new triangle A1B1C1 A B C A1 B1 C1 O
Centre of rotation

11. The centre of rotation can be in different places
Rotate triangle ABC about O through to get a new triangle A1B1C1 A1 B1 C1
Centre of rotation O

12. Enlargement
An enlargement changes the size of an object. The change is the same in all directions
Enlarge the rectangle by a scale factor of 2
6 squares
4 squares
3 squares
2 squares

13. Enlargements are normally done from a centre of enlargement.
Enlarge the triangle ABC by a scale factor 2. Use O as the centre of enlargement.
Measure the distance from the centre O to the vertex A on the triangle C1 A B C
Then multiply this distance by the scale factor. Label this point A1 B1 A1
Repeat for the other vertices B and C O

14. The centre of enlargement does not always have to be in the same place
Enlarge the triangle ABC by a scale factor 3. Use O as the centre of enlargement. A B C O A1 B1

15. The scale factor can also be less than 1
Enlarge the triangle ABC by a scale factor . Use O as the centre of enlargement. A B C C1 B1 A1 O

16. The scale factor can also be less than 0
Enlarge the triangle ABC by a scale factor -2. Use O as the centre of enlargement. A1 O
Notice that the image A1B1C1 is inverted B1 C1

17. To find the mirror line of a reflection given the object and its image
Join two corresponding points on the object and its image AA1 A1 B1 C1 A B C
Construct the perpendicular bisector of this line segment
Perpendicular bisector of AA1 i.e. mirror line

18. To find the centre of rotation given an object and its image
Join two corresponding points on the object and its image AA1 A B C
Draw the perpendicular bisector of this line segment A1 B1 C1
Repeat for two other corresponding points BB1
Centre of rotation