Pre-Calculus Homework Solutions 81

Pre-Calculus Homework Solutions 81 - 22. The slope of a...

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22. The slope of a line perpendicular to y 5 2 x 2 1 and y 5 2 x 1 9 is 2 } 1 2 } .Use the y -intercept of y 5 2 x 2 1, (0, 2 1), as one of the endpoints of the perpendicular segment. y 2 y 1 5 ¬ m ( x 2 x 1 ) y 2 ( 2 1) 5 ¬ 2 } 1 2 } ( x 2 0) y 1 1 5 ¬ 2 } 1 2 } x y 5 ¬ 2 } 1 2 } x 2 1 Use a system of equations to determine the point of intersection of the line y 5 2 x 1 9 and the perpendicular segment. 2 x 1 9 5 ¬ 2 } 1 2 } x 2 1 2 x 1 } 1 2 } x 5 ¬ 2 1 2 9 } 5 2 } x 5 ¬ 2 10 x 5 ¬ 2 4 y 5 ¬ 2( 2 4) 1 9 y 5 ¬ 1 The point of intersection is ( 2 4, 1). Use the Distance Formula to determine the distance between (0, 2 1) and ( 2 4, 1). d 5 ¬ Ï ( x 2 2 w x 1 ) 2 1 w ( y 2 2 w y 1 ) 2 w 5 ¬ Ï ( 2 4 2 w 0) 2 1 w [1 2 ( w 2 1)] 2 w 5 ¬ Ï ( 2 4) 2 w 1 2 2 w 5 ¬ Ï 20 w The distance between the lines is Ï 20 w or about 4.47 units. 23. The slope of a line perpendicular to y 52 x 1 4 and y 52 x 2 2 is 1. Use the y -intercept of y 52 x 1 4, (0, 4), as one of the endpoints of the
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