Pre-Calculus Homework Solutions 75

Pre-Calculus Homework Solutions 75 - 3 4x 23. 2x y 4 y 2x 4...

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23. 2 x 2 y 5 ¬ 2 4 2 y 5 ¬ 2 2 x 2 4 y 5 ¬ 2 x 1 4 First, write an equation of a line p perpendicular to the lines y 5 2 x 2 3 and y 5 2 x 1 4. The slope of p is the opposite reciprocal of 2, or 2 } 1 2 } .Use the y -intercept of the line y 5 2 x 2 3, (0, 2 3), as one of the endpoints of the perpendicular segment. y 2 y 1 5 ¬ m ( x 2 x 1 ) y 2 ( 2 3) 5 ¬ 2 } 1 2 } ( x 2 0) y 1 3 5 ¬ 2 } 1 2 } x y 5 ¬ 2 } 1 2 } x 2 3 Next, use a system of equations to determine the point of intersection of the line y 5 2 x 1 4 and p. 2 x 1 4 5 ¬ 2 } 1 2 } x 2 3 2 x 1 } 1 2 } x 5 ¬ 2 3 2 4 } 5 2 } x 5 ¬ 2 7 x 5 ¬ 2 } 1 5 4 } y 5 ¬ 2 1 2 } 1 5 4 } 2 1 4 y 5 ¬ 2 } 8 5 } The point of intersection is 1 2 } 1 5 4 } , 2 } 8 5 } 2 . Then, use the Distance Formula to determine the distance between (0, 2 3) and 1 2 } 1 5 4 } , 2 } 8 5 } 2 . d 5 ¬ Ï ( x 2 2 w x 1 ) 2 1 w ( y 2 2 w y 1 ) 2 w 5 ¬ ! 1 2 } 1 5 4 } § 2 0 2 2 § 1 3 2 } 8 5 § } 2 ( 2 § 3) ± 2 § 5 ¬ ! 1
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.

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