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Unformatted text preview: Math 466 - Homework Set 1 (1.10.2011) 1. Which of the mappings defined on the Cartesian plane by the equa- tions below are transformations? (a) f ( x,y ) = ( cos x,sin y ) , (b) g ( x,y ) = (3 y,x + 2) . 2. Which of the transformations (if any) in exercise 1 are collineations? 3. Write the definitions of transformation, collineation, involution, trans- lation, isometry, dilatation and halfturn . 4. Let P = (- 1 , 2) and Q = (3 ,- 5) . (a) Write the equations for the translation that maps P to Q . (b) Find the formula for the halfturn σ P . (c) If ‘ is the line with an equation y = 1- x find τ P,Q ( ‘ ) . (d) Let 4 ABC be the triangle with vertices A = (0 , 0) , B = (2 , 0) and C = (1 , 2) . If R = (0 , 1) find σ R ( 4 ABC ) and draw the image. 5. Let M = ( a,b ) be a point in R 2 . Find equations for u and v where f ( x,y ) = ( u,v ) and f is the mapping such that for any point P the midpoint of the segment joining P and f ( P ) is always M ....
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