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geometry q: where is line k??

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fdv
 Post subject: geometry q: where is line k??
 Post Posted: Sun Aug 10, 2008 11:55 am 
Hi, the answer to q below is 90 degrees. i understand that lines L and W are perpendicular but why is line k perp? my answer was E as there is no info on K. What am I missing? Please advise. thanks!

Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w?
0

30

60

90

It cannot be determined from the information given.
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TP
 Post subject: Re: geometry q: where is line k??
 Post Posted: Wed Aug 13, 2008 11:11 am 
fdv wrote:
Hi, the answer to q below is 90 degrees. i understand that lines L and W are perpendicular but why is line k perp? my answer was E as there is no info on K. What am I missing? Please advise. thanks!

Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w?
0

30

60

90

It cannot be determined from the information given.


If k does not intersect line l it must be parallel to line l, hence perpendicular to like w.
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fdv
 Post subject:
 Post Posted: Thu Aug 14, 2008 1:51 am 
thank you. i overlooked the fact that they should intersect if not parallel.
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jwinawer
 Post subject:
 Post Posted: Sat Sep 20, 2008 3:03 am 
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ManhattanGMAT Staff


Posts: 76
nice work tp. that's right - they buried a little trick about parallel lines into that one!
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sumit
 Post subject: jonathan /fdv
 Post Posted: Wed Sep 24, 2008 6:48 am 
hi

can u pls confirm if your conclusion that line l and w are perp. is based only on the fact that the product of their slopes is -1?

Is this a firm principle, are there any more such principles to take note of in case of lines?
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esledge
 Post subject: Rules about slope of lines
 Post Posted: Mon Oct 27, 2008 2:04 pm 
Offline
ManhattanGMAT Staff


Posts: 901
Location: St. Louis, MO
Hi Sumit,

Yes, you can conclude that lines l and w are perpendicular based solely on their respective slopes.

line l: y = 5x + 4, slope = 5.
line w: 10y = -2x - 20, so y = (-1/5)x - 2, slope = -1/5.

The product of the slopes of perpendicular lines is always -1, as is true here: (5)(-1/5) = -1.

The only other rule about slopes is that parallel lines have the same slope as each other. That rule was used in this problem, too. Line k is parallel to line l, so line k has slope = 5.

_________________
Emily Sledge
Instructor
ManhattanGMAT
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