Unformatted text preview: 6. Let O λ be a dilation with centre O and scaling factor λ , where λ 6 = 0 , 1. Show that O λ commutes with a reﬂection r ` across a line ` through O . This is called a dilative reﬂection. Show also that O λ commutes with a rotation R O,θ about O . This is called a dilative rotation. 7. Let O λ and O μ be two dilations about distinct points O and O with scaling factors λ and μ , respectively, with λ 6 = 0 , 1 and μ 6 = 0 , 1. Suppose further that λμ 6 = 1. Show that the composition O μ ◦ O λ is again a dilation with scaling factor λμ . Show that the centre P of this dilation lies on the line ←→ OO such that the OP = ± ± ± μ1 λμ1 ± ± ± OO , with P and O on the same side of O if μ1 λμ1 > 0 and P , O on opposite sides of O if μ1 λμ1 < 0. What happens when λμ = 1? 1...
View
Full
Document
This note was uploaded on 02/20/2011 for the course MATH 348 taught by Professor Karigiannis during the Summer '06 term at McGill.
 Summer '06
 Karigiannis
 Geometry, Angles

Click to edit the document details