Lesson Notes By Weeks and Term v4 - SHS 3

Lesson Video

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Performance objectives

• Define and explain translation, reflection, rotation, and enlargement.
• Apply linear transformations to perform translations of points.
• Calculate the images of points under reflections.
• Determine the new coordinates of points after rotation.
• Use enlargement to find the image of a figure under a given scale factor.

Lesson summary

This lesson introduces students to the fascinating world of linear transformations. We will explore how algebraic tools, specifically vectors and matrices, can be used to describe geometric movements like sliding, flipping, turning, and resizing. These concepts are not just abstract mathematics; they are the foundation of computer graphics, video game design, animation, and even the beautiful repeating patterns found in Ghanaian Kente cloth and Adinkra symbols. By understanding the algebra behind these movements, we gain the power to precisely control and manipulate shapes in a two-dimensional plane.

Lesson notes

Introduction: What is a Transformation? In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. The original shape is called the object. The new shape after the transformation is called the image. We often denote the image of a point P as P' (read as "P prime").

We will represent points like P(x, y) as column vectors: `[x; y]`. This allows us to use matrix algebra to perform transformations. The general rule for most transformations (except translation) is:

Image = Transformation Matrix × Object `[x'; y'] = M * [x; y]`

Let's explore the four main types of linear transformations. A. Translation (A "Slide") A translation slides every point of a shape the same distance in the same direction. It is defined by a translation vector, T. Translation is unique because it uses vector addition, not matrix multiplication. Rule: `Image = Object + Translation Vector` If an object point is P(x, y) and the translation vector is `T = [a; b]`, then the image point P'(x', y') is given by: `[x'; y'] = [x; y] + [a; b] = [x + a; y + b]` The top number in the vector `(a)` tells you how much to move horizontally (positive for right, negative for left). The bottom number `(b)` tells you how much to move vertically (positive for up, negative for down).

Evaluation guide

• Apply linear transformation in finding translation, reflections, rotations and enlargement
• of points and plane figures.
• Think -pair- share, Talk for Learning, and Building on what others say.
• perform translation of points.