2 . This question aims at investigating the changes of plane figures in a sequence of slides .
Alfred , Benny and Calix are creating presentation slides showing the sequence of the changes of a plane figure . On the first slide , an isosceles triangle PQR is constructed on a coordinate plane such that PR � QR , and the coordinates of P and Q are ( 10 , 0 ) and ( 0 , � 10 ) respectively .
y
O
P x
Q R
( a ) Write down
( i ) the coordinates of R ;
( ii ) the area of the triangle PQR .
Alfred and Benny plan to generate the next slide by applying the transformation
� x � � x � � A 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 ( x , y ) is its image after n transformations , A n is a 2� 2 matrix representing n n n an enlargement about the origin , with a variable scale factor k( n) �a� b , a , b� .
Alfred suggests a � 2 and b � 1. Let ( x0, y
0) be the coordinates of R .
[ 2 ]
( b ) ( i ) Find
�x �
3
� � �y3
� .
( ii ) Find the area of the triangle P3Q 3R 3 , the image of PQR after 3 transformations .
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