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Unformatted text preview: 6. Let O be a dilation with centre O and scaling factor , where 6 = 0 , 1. Show that O commutes with a reection r ` across a line ` through O . This is called a dilative reection. Show also that O commutes with a rotation R O, about O . This is called a dilative rotation. 7. Let O and O be two dilations about distinct points O and O with scaling factors and , respectively, with 6 = 0 , 1 and 6 = 0 , 1. Suppose further that 6 = 1. Show that the composition O O is again a dilation with scaling factor . Show that the centre P of this dilation lies on the line  OO such that the OP = 1 1 OO , with P and O on the same side of O if 1 1 > 0 and P , O on opposite sides of O if 1 1 < 0. What happens when = 1? 1...
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 Summer '06
 Karigiannis
 Geometry, Angles

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