Lesson Notes By Weeks and Term v4 - JHS 2

Lesson Video

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Performance objectives

• Identify coordinates of points in a coordinate plane.
• Rotate a point around the origin by a given angle.
• Draw the rotated image of a shape.
• Calculate the angle of rotation for a given transformation.

Lesson summary

This lesson introduces learners to rotation, which is a type of transformation. Rotation is simply the turning of an object around a fixed point. We see rotation everywhere in our daily lives in Ghana – from the blades of a standing fan in our homes, to the wheels of a tro-tro, to the beautiful rotational patterns in Adinkra symbols like *Gye Nyame*. By the end of this lesson, you will be able to perform and describe these turns mathematically on a graph (the Cartesian or coordinate plane). This skill is important not only in mathematics but also in fields like engineering, art, and computer graphics.

Lesson notes

A. What is Rotation?

Rotation is a transformation that turns a shape or a point around a fixed point. This is different from reflection (flipping) or translation (sliding). To describe a rotation fully, we need three pieces of information: The Centre of Rotation: This is the fixed point that the shape turns around. It does not move. In JHS 2, our centre of rotation will almost always be the origin (0, 0). The Angle of Rotation: This tells us how far the shape has turned. We will focus on the most common angles: 90° (a quarter turn), 180° (a half turn), and 270° (a three-quarter turn). The Direction of Rotation: This tells us which way the shape is turning. Anticlockwise (or Counter-clockwise): This is the opposite direction to how the hands of a clock move. In mathematics, this is considered the positive direction. Clockwise: This is the same direction that the hands of a clock move. This is considered the negative direction.

*Note:* A 90° anticlockwise turn is the same as a 270° clockwise turn. A 90° clockwise turn is the same as a 270° anticlockwise turn. A 180° turn is the same in both directions. B. Rules for Rotation About the Origin (0, 0)

Instead of using a protractor and compass, we can use simple rules to find the new coordinates of a point after rotation. Let's say we have a point P(x, y). The new point after rotation is called the image, P'(x', y').