EDEXCEL GCSE FOUNDATION MATHS - What are Translations

Edexcel GCSE Foundation Maths: Translations

What is a Translation?

A translation is a movement of a shape without any rotation or reflection. It's simply sliding the shape in a specific direction.

Key Points:

• Direction: A translation is defined by a vector. A vector tells you how many units to move the shape horizontally and vertically.
• Size and Shape: The shape remains the same size and shape after a translation. Only its position changes.

Representing Translations:

• Vectors: Translations are often represented using a vector. For example, the vector (2, 3) tells you to move the shape 2 units to the right and 3 units up.

• Arrow Notation: Another way to show a translation is by drawing an arrow from a point on the original shape to the corresponding point on the translated shape.

Example:

Let's say we have a triangle with vertices at points A(1, 1), B(3, 1), and C(2, 3). We want to translate this triangle using the vector (4, -2).

1. Apply the Vector: Add the vector's components to the coordinates of each vertex:

   • A(1, 1) + (4, -2) = A'(5, -1)
   • B(3, 1) + (4, -2) = B'(7, -1)
   • C(2, 3) + (4, -2) = C'(6, 1)

2. Plot the Translated Shape: Plot the new points A'(5, -1), B'(7, -1), and C'(6, 1) to form the translated triangle.

Key Concepts to Remember:

• Direction: The vector determines the direction of the translation.
• Magnitude: The size of the vector components determines how far the shape moves.
• Congruence: The original shape and its translated image are congruent (same size and shape).

Practice:

1. Translate a square using the vector (-3, 1).
2. Draw an arrow showing a translation of a rectangle using the vector (2, -4).

By understanding translations, you'll be well-equipped to solve geometry problems involving transformations in Edexcel GCSE Foundation Maths.