Chapter 11: Isometric Transformations
What you need to learn in this chapter
In this chapter, we will be learning about isometric transformations. Isometric transformations are changes that happen to shapes, sizes, directions, and orientations of an object. We will learn about the concept of one-to-one correspondence between points in a transformation, which means that each point in the original shape corresponds to a unique point in the transformed shape. We will also learn about congruency in transformations, which means that the transformed shape is the same size and shape as the original shape. Additionally, we will study translations, which are movements of shapes without changing their size or shape. We will also learn about reflection, which is a transformation that flips a shape over a line, and rotation, which is a transformation that turns a shape around a fixed point.
Topics in this chapter
1. Transformation
What you will learn in this topic
- Describe the changes of shapes, sizes, directions and orientations of an object under a transformation, and hence explain the idea of one-to-one correspondence between points in a transformation.
- Explain the idea of congruency in transformations
2. Translations
What you will learn in this topic
- Recognise a translation
- Describe translation by using various representations including vector form
- Determine the image and object under a translation
- Solve problems involving translation
3. Reflection
What you will learn in this topic
- Recognise a reflection
- Describe reflection using various representations
- Determine the image and object under a reflection
- Solve problems involving reflection
4. Rotation
What you will learn in this topic
- Recognise a rotation
- Describe rotation using various representations
- Determine the image and object under a rotation
- Solve problems involving rotation
5. Translation, Reflection and Rotation as an Isometry
What you will learn in this topic
- Investigate the relationship between the effects of translation, reflection and rotation and the distance between two points on an object and image, and hence explain isometry
- Explain the relationship between isometry and congruency
- Solve problems involving isometry and congruency
6. Rotational Symmetry
What you will learn in this topic
- Explain rotational symmetry
- Determine the order of rotational symmetry of an object
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