Intern
Joined: 28 Aug 2007
Posts: 19
Location: London, United Kingdom
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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 coordinates 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 coordinates 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 coordinates (1/2; 1/2).
Substitute these coordinates 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?
