Study Notes
Transformation geometry involves changing the position and/or size of a shape using specific methods.
- 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 from a center point. Example: The letter T is enlarged by a scale factor of 2 using point O as the center.
- Stretch — altering the shape by stretching it in a specific direction with a stretch factor. Example: Rectangle ABCD is stretched parallel to the y-axis with a factor of 2.
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 described by a vector.
- Enlargement: Changing size with a scale factor from a center.
- Stretch: Altering shape by stretching in a direction.
Common Confusions
- Confusing rotation direction (clockwise vs anticlockwise).
- Mixing up translation vectors with coordinates.
- Misidentifying the center of enlargement.
Typical Exam Questions
- How do you describe a reflection? Provide the equation of the mirror line.
- What is needed to describe a rotation? The angle and center of rotation.
- How do you describe an enlargement? Give the scale factor and center of enlargement.
What Examiners Usually Test
- Ability to identify and describe transformations.
- Use of vectors to describe translations.
- Understanding of combined transformations.