( iii ) Show that x
2
52 n � n
� yn
� � .
Benny suggests a � 1 and b � 1.1. Let ( x0, y
0) be the coordinates of Q .
[ 11 ]
( c ) ( i ) Find
�x �
4
� � �y4
� .
( ii ) Find the least value of n such that yn
�� 375.
Calix plans to generate the next slide by applying the transformation � x � � x � � B n
0
� � n � � � yn
� � y0 � to the current slide , where n � 1 is the number of slides after
the first slide , ( x0, y
0) is a point on the triangle PQR where ( xn, y n) is its image after n transformations , about the line y �( tan ( n� 45 )) x .
B n is a 2� 2 matrix representing a reflection
[ 10 ]
Note : The line of reflection is defined as x � 0 when n is even .
( d ) ( i ) Express B
2 as the product of two matrices .
( ii ) On the following diagram , sketch the triangle P2Q 2R 2 , the image of the triangle PQR after two transformations .
y
[ 3 ]
O x
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