Apps. and Interpretation HL Practice Paper Book | Page 29

www . seprodstore . com 17 � Two-dimensional transformation matrices : 1 . 1 0 0 1 � � � � � � � : Reflection about the x -axis 2 . 1 0 0 1 � � � � � � � : Reflection about the y -axis 3 . cos 2 sin 2 sin 2 cos 2 � � � � � � � � � � � : Reflection about the line y mx � , where tan m � � 4 . 1 0 0 k � � � � � � : Vertical stretch with scale factor k 5 . 0 0 1 k � � � � � � : Horizontal stretch with scale factor k 6 . 0 0 k k � � � � � � : Enlargement about the origin with scale factor k 7 . cos sin sin cos � � � � � � � � � � � : Rotation with positive angle � anticlockwise about the origin 8 . cos sin sin cos � � � � � � � � � � � : Rotation with positive angle � clockwise about the origin 9 . Area of the image det ( ) T � � Area of the object , where T is the transformation matrix � Terminologies of vectors : AB ^� : Vector of length AB with initial point A and terminal point B OP ^� : Position vector of P , where O is the origin AB ^� : Magnitude ( length ) of AB ^� 1 ˆ � v v v : Unit vector parallel to v , with ˆ 1 � v 0 : Zero vector i : Unit vector along the positive x -axis j : Unit vector along the positive y -axis k : Unit vector along the positive z -axis 17 ^Vectors