hw11sol - Homework 11 1. Let A = (0 , 0) let B = (2 , 1)....

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Unformatted text preview: Homework 11 1. Let A = (0 , 0) let B = (2 , 1). (i) Find a line so that ( B ) = B = (3 , 4). (ii) Fine a line m so that m 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 = ( A ). Our first goal will be to find A , and then we will find a suitable line m so that m ( A ) = m ( 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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hw11sol - Homework 11 1. Let A = (0 , 0) let B = (2 , 1)....

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