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CEO
Joined: 21 Jan 2007
Posts: 2797
Location: New York City
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What is the equation of the line that is perpendicular to [#permalink]
 21 Nov 2007, 06:28
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What is the equation of the line that is perpendicular to line y=2x and passes through point (a,b)?
1. a = -b
2. a - b = 1
Please EXPLAIN your answer
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Intern
Joined: 28 Aug 2007
Posts: 19
Location: London, United Kingdom
Followers: 1
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I'll give it a go...
The slope of a line perpendicular to another line is equal to minus the reciprocal of the slope of the line to which it is perpendicular.
Therefore the slope of the line perpendicular to y = 2x is -1/2
Therefore the equation of the perpendicular line is y = -1/2x + k
Statement 1: a = -b This is insufficient, as there are an infinite number of co-ordinates that match this criterion, e.g. (-1, 1), (1,-1), (2,-2), (-2,2), etc.
Statement 2: a - b = 1 This is insufficient, as again there are an infinite number of co-ordinates that match this criterion.
Statements 1 and 2 together: subsitute the equation in Statement 2 into the equation in Statement 1 and solve for b:
(1 + b) = -b
1 = -2b
b = -1/2
Subsitute into either equation to solve for a:
a = 1/2
Therefore the perpendicular line goes through co-ordinates (1/2; -1/2).
Substitute these co-ordinates into the equation of the perpendicular line and solve for k:
y = -1/2x + k
(-1/2) = -1/2(1/2) + k
-1/2 = -1/4 + k
- 2/4 + 1/4 = k
k = -1/4
Therefore equation of perpendicular line is y = -1/2x - 1/4
Therefore answer is C?
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CEO
Joined: 21 Jan 2007
Posts: 2797
Location: New York City
Followers: 5
Kudos [?]:
132
[0], given: 4
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OA is C. 
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