Study Notes
In transformation geometry, objects are moved or changed in position or size without altering their shape. Transformations include reflection, rotation, translation, and enlargement.
- Reflection — a mirror image of an object across a line. Example: The purple triangle is a reflection of the blue triangle in the line x=2.
- Rotation — turning an object around a point by a certain angle and direction. Example: The purple triangle is rotated 180° clockwise around the point (2, 1).
- Translation — moving an object in a straight line described by a vector. Example: Triangle ABC is translated 7 squares right and 2 squares up to become triangle A'B'C'.
- Enlargement — changing the size of an object using a scale factor and a centre of enlargement. Example: The letter T is enlarged by a scale factor of 2 using point O as the centre.
Exam Tips
Key Definitions to Remember
- Reflection: A mirror image across a line.
- Rotation: Turning around a point by an angle.
- Translation: Moving in a straight line by a vector.
- Enlargement: Changing size by a scale factor.
Common Confusions
- Confusing clockwise and anticlockwise directions in rotations.
- Mixing up translation vectors with coordinates.
Typical Exam Questions
- What is the reflection of a triangle across the line x=3? The triangle's mirror image will be on the opposite side of x=3.
- How do you describe a rotation of 90° anticlockwise around the origin? The object is turned 90° in the positive direction around the origin.
- What is the translation vector for moving a shape 5 units left and 3 units down? The vector is (-5, -3).
What Examiners Usually Test
- Ability to identify and describe different transformations.
- Understanding of how transformations affect the position and size of shapes.