Rotation | Mathematics Form 2

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Rotation - Mathematics Form 2












 


Lesson Objectives

By the end of the lesson, you should be able to:


1.Determine the centre and angle of rotation in the Cartesian plane


2. Determine the image given the objects and centre.


3. State the order of rotational symmetry of a plane figure





Introduction

CENTRE AND ANGLE OF ROTATION

When the coordinates of an object and image are given, to get the centre and angle of rotation, the following steps are important:

(i)Join two object points to their corresponding image points i.e. A to A' and B to B'.

(ii)Construct the perpendicular bisectors of the line segments AA' and BB'.

(iii)The point of intersection of the two perpendiculars gives the centre of rotation. Mark it as point O.

(iv)Read off the coordinates of O.

(v)To get the angle of rotation, join either A to O (Object line) and O to A' (image line) or B to O and O to B'. Angle AOA' or BOB' is the angle of rotation.

(vi)The angle of rotation is measured form the object line through the centre of rotation to the image line. If the direction for the object line to image line is clockwise the angle is negative and if it is in an anticlockwise direction, the angle is positive.

Worked Examples

Example 1

Triangle ABC has coordinates A(2,3), B(2,1) and C(3,1). After rotation, it has its image in triangle A'B'C' whose coordinates are A'(-3,2), B' (-1,2) and C'(-1,3).

(i)Plot on the same axis,triangle ABC and triangle A'B'C'.

(ii)Find the coordinates of the centre of rotation

(iii)State the angle of rotation

(iv)Describe the rotation























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