Apps. and Interpretation for IBDP Maths Ebook 2 | Page 97

www . seprodstore . com 87 7 The transformation S and T are represented by the matrices 0 1 1 0 � � � � � � � and 3 1 2 2 1 3 2 2 � � � � � � � � � � � � � respectively . ( a ) Find ST . [ 2 ] ( b ) Describe the transformation represented by ST . [ 1 ] ( c ) ST transforms the point ( 2 , 4 ) to the point P . Find the coordinates of P . [ 2 ] ( a ) 3 1 0 1 2 2 1 0 1 3 2 2 � � � � � � � � � � � � �� � � � � � � � ST 1 3 2 2 3 1 2 2 � � � � � � � � � � � � � � � � ST A2 [ 2 ] ( b ) Rotation anticlockwise of 2 3 � radians about the origin . A1 [ 1 ] ( c ) 1 3 2 2 2 4 3 1 2 2 x y � � � � � � � � � � � � � � � � � � � � � � � � � � � � ( M1 ) for valid approach 4.464101615 0.2679491924 x y � � � � � � � � � � � � � � � Thus , the coordinates of P are ( 4.46 , 0.268 ) � � . A1 [ 2 ] Example Solution 28 Paper 1 – Transformation Matrices

www . seprodstore . com 87 7 The transformation S and T are represented by the matrices 0 1 1 0 � � � � � � � and 3 1 2 2 1 3 2 2 � � � � � � � � � � � � � respectively . ( a ) Find ST . [ 2 ] ( b ) Describe the transformation represented by ST . [ 1 ] ( c ) ST transforms the point ( 2 , 4 ) to the point P . Find the coordinates of P . [ 2 ] ( a ) 3 1 0 1 2 2 1 0 1 3 2 2 � � � � � � � � � � � � �� � � � � � � � ST 1 3 2 2 3 1 2 2 � � � � � � � � � � � � � � � � ST A2 [ 2 ] ( b ) Rotation anticlockwise of 2 3 � radians about the origin . A1 [ 1 ] ( c ) 1 3 2 2 2 4 3 1 2 2 x y � � � � � � � � � � � � � � � � � � � � � � � � � � � � ( M1 ) for valid approach 4.464101615 0.2679491924 x y � � � � � � � � � � � � � � � Thus , the coordinates of P are ( 4.46 , 0.268 ) � � . A1 [ 2 ] Example Solution 28 Paper 1 – Transformation Matrices