Translations | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Translations

What are transformations in maths?

• In GCSE Maths, there are four fundamental transformations: rotation, reflection, translation, and enlargement.
• Each of these transformations alters a shape in a distinct manner, making them valuable tools in applications like computer graphics.
• Within this topic, specific language and notation are commonly employed. The original shape is referred to as the object, while the transformed shape is termed the image.
• Vertices are labeled to denote corresponding points:
  • Vertices on the object are denoted as A, B, C, etc.
  • Vertices on the image are denoted as A', B', C', etc.
  • If a second transformation occurs, these vertices may be labeled as A", B", C", etc.

What is a translation?

• Translation refers to the process of moving a shape from one location to another.
• During translation, the size, shape, and orientation of the shape remain unchanged.

How do I translate a shape?

• A translation's motion is described by a vector.
• To express a translation using a vector, the vector is represented as a column vector with two components:
  • The horizontal distance moved (x): A negative value denotes a leftward movement, while a positive value indicates a rightward movement.
  • The vertical distance moved (y): A negative value signifies a downward movement, whereas a positive value represents an upward movement.
• Step 1 involves selecting a vertex on the original object and moving it according to the information provided in the column vector.
• Step 2 requires repeating Step 1 for each vertex on the original object.
• In Step 3, the translated vertices are connected, and the translated image is labeled.
• In some instances, when vectors are sufficiently small, the image may overlap with the object.
• It's crucial to recognize that the vector signifies the shape's movement, not the size of the gap between the object and the image, which is a common error to avoid.

How do I describe a translation?

• Fully describing a transformation is essential for achieving full marks. Specifically, for a translation, the following steps are necessary:
  • Clearly state that the transformation being performed is a translation.
  • Provide the column vector that precisely describes the movement undergone by the shape.
• Ensuring these two components are included in the description is vital for comprehensive understanding and accuracy in assessing the transformation.