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In the xy – plane, what is the slope of line perpendicular

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In the xy – plane, what is the slope of line perpendicular [#permalink] New post 23 Jan 2011, 10:38
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In the xy – plane, what is the slope of line perpendicular to line K?

(1) line K intersects line with equation 2x + 3y = 4 at point Q (2,0)
(2) Line K does not intersect line with equation y = 2x-5
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Re: what is the slope of line perpendicular to line K? [#permalink] New post 23 Jan 2011, 11:04
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MichelleSavina wrote:
Q) In the xy – plane, what is the slope of line perpendicular to line K?
(1) line K intersects line with equation 2x + 3y = 4 at point Q (2,0)
(2) Line K does not intersect line with equation y = 2x-5


In the xy – plane, what is the slope of line perpendicular to line K?

You should know 2 important things:

1. For one line to be perpendicular to another, the relationship between their slopes has to be negative reciprocal, so if the slope of one line is m then the line prependicular to it will have the slope -\frac{1}{m}. In other words, the two lines are perpendicular if and only the product of their slopes is -1.

2. Parallel lines have the same slope.

(1) line K intersects line with equation 2x + 3y = 4 at point Q (2,0) --> clearly insufficient, as we don't know the angle at which the line K intersects this line (we just have some line and know that K intersect it at some point). Not sufficient.

(2) Line K does not intersect line with equation y = 2x-5 --> K is parallel to this line so has the same slope --> slope of K=2 --> the line perpendicular to line K will have the slope -1/2. Sufficient.

Answer: B.

For more on these issues check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: In the xy – plane, what is the slope of line perpendicular [#permalink] New post 01 May 2012, 23:52
If the statement says that ==> Line K does not intersect line with equation y = 2x-5--> K is parallel to this line so has the same slope. How do I know that these two lines are parallel?
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Re: In the xy – plane, what is the slope of line perpendicular [#permalink] New post 02 May 2012, 00:02
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Stiv wrote:
If the statement says that ==> Line K does not intersect line with equation y = 2x-5--> K is parallel to this line so has the same slope. How do I know that these two lines are parallel?


From definition: two lines in a plane that do not intersect are called parallel lines.

So, K does not intersect line with equation y = 2x-5 means that these lines are parallel.
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Re: In the xy – plane, what is the slope of line perpendicular [#permalink] New post 03 May 2012, 04:41
Thanks, this was helpful!
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Re: In the xy – plane, what is the slope of line perpendicular [#permalink] New post 31 Aug 2013, 05:23
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Re: In the xy – plane, what is the slope of line perpendicular   [#permalink] 31 Aug 2013, 05:23
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