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# What is the equation of the line that is perpendicular to

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CEO
Joined: 21 Jan 2007
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What is the equation of the line that is perpendicular to [#permalink]

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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

Intern
Joined: 28 Aug 2007
Posts: 19
Location: London, United Kingdom
Followers: 1

Kudos [?]: 1 [0], given: 0

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21 Nov 2007, 07:16
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?
CEO
Joined: 21 Jan 2007
Posts: 2745
Location: New York City
Followers: 11

Kudos [?]: 942 [0], given: 4

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23 Nov 2007, 10:51
OA is C.
23 Nov 2007, 10:51
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# What is the equation of the line that is perpendicular to

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