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Unformatted text preview: Homework 11 1. Let A = (0 , 0) let B = (2 , 1). (i) Find a line ‘ so that σ ‘ ( B ) = B = (3 , 4). (ii) Fine a line m so that σ m σ ‘ maps B to (3 , 4) and A to (1 , 5). Solution: (i): the line ‘ is the perpendicular bisector of B = (2 , 1) and B = (3 , 4). We see that BB has slope 4 1 3 2 = 3 so ‘ has slope 1 3 . Further, ‘ must contain the midpoint of BB which is the point ( 2+3 2 , 1+4 2 ) = ( 5 2 , 5 2 ). It follows that ‘ is given by the equation Y 5 2 = 1 3 ( X 5 2 ). (ii): Set A = σ ‘ ( A ). Our first goal will be to find A , and then we will find a suitable line m so that σ m ( A ) = σ m σ ‘ ( A ) is the desired point. Declare p to be the line through A with slope 3. Then the point A must lie on the line p and the midpoint of A and A is the intersection point of p and ‘ . To find this intersection point, we first an equation for p . This is easy, it passes through A = (0 , 0) and has slope 3 so p is given by Y = 3 X . Now, the intersection of p and...
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This note was uploaded on 01/30/2012 for the course MATH 310 303 taught by Professor Rwk during the Spring '11 term at Simon Fraser.
 Spring '11
 RWK

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