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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]

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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]

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New post 23 Jan 2011, 12:04
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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]

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New post 02 May 2012, 00:52
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]

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New post 02 May 2012, 01:02
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]

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New post 03 May 2012, 05:41
Thanks, this was helpful!
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Re: In the xy – plane, what is the slope of line perpendicular [#permalink]

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New post 22 Oct 2017, 22:14
Answer should be B,

A. line K intersects line with equation 2x + 3y = 4 at point Q (2,0) - Dont know how much angle it is crating- Not sufficient.
B. Line K does not intersect line with equation y = 2x-5, means parallel lines - Sufficient
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Re: In the xy – plane, what is the slope of line perpendicular   [#permalink] 22 Oct 2017, 22:14
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