1. Matrix corresponding to rotation Matrix corresponding to reflection Rotation and reflection y=(tan  )x 

2. Example 1 - Rotation Let f be a linear transformation given by (a)Find the matrix corresponding to the linear transformation. (b)Show that f corresponds to a rotation through an angle  about the origin. Find . (a) Since the matrix is (b) Hence  =306.9 o.

3. Example 2 - Rotation If A(7,6) is rotated through an acute angle , where tan  = 0.75, about the point B(3,4), to a new position C(x,y), find C.  Matrix corresponding to the rotation 3 4 5 

4. Example 3 - Reflection Find the reflection of the point (2,1) about the line y = 3x. Reflection about the line y = (tan  )x  Since tan  =3,

5. Example 4 - pg 21 f g Reflection about the line y = x followed by Rotation through 60 o about the origin 60 o y=x

6. Show that this is equivalent to a reflection about a line. Hence 2  =150 o,  =75 o. Solution

7. 150 o -  2  Geometrical Interpretation 60 o y=x  45 o -   y = (tan75 o )x 75 o -  equivalent to a reflection about the dotted line first reflection then rotation