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Senior Manager
Joined: 14 Jun 2007
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at what angle do lines y=Kx+L and x=y+KL intersect? I K=2 II
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23 Jun 2007, 10:57
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at what angle do lines y=Kx+L and x=y+KL intersect?
I K=2
II K=L
SPOILER:
I understand that slope of y=x+KL = 1 and from I we have the slope of the other line = 2. The OA is A, but i dont understand how that is enough to figure out the angle. the slopes are not negative reciprocals therefore they aren't perpendicular... so someone please explain thanks == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



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Joined: 21 May 2007
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y=2x+L and x=y+KL
are sets of parallel lines, where L and KL define only the intercepts.
Lines from any one set will intersect lines from the other set at same angle.
hope that helps
best,
Parsifal



Senior Manager
Joined: 14 Jun 2007
Posts: 392

parsifal wrote: y=2x+L and x=y+KL are sets of parallel lines, where L and KL define only the intercepts.
Lines from any one set will intersect lines from the other set at same angle.
hope that helps
best, Parsifal
parsifal;
two points i wanted to make  parallel lines never intersect  if paralell lines 'intersect' they are the same line and are intersecting across infinite points. in that case i guess we can figure out the angle of intersection (180?)
point two is that parallel lines have the same slope
y=2x+L has a slope of 2
x=y+KL = y=KLx = y=xKL
y=xKL has slope of 1
therefore they aren neither parallel nor perpendicular; so how do we derive the angle of intersection?
from



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Posts: 1135

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Updated on: 23 Jun 2007, 23:26
I personally think this problem is way out of scope, but here we go:
at what angle do lines y=Kx+L and x=y+KL intersect ?
Y = KX+L
Y = XKL
knowing the two slopes , we can determine the intersect angle, see Fig post:
http://www.gmatclub.com/phpbb/viewtopic.php?t=42333
statement 1
K=2
slopes (2,1)
sufficient
statement 2
Y = KX+L
Y = XKL
we can't find the slopes (K,1) so:
insufficient



Manager
Joined: 21 May 2007
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@anonymousegmat:
I never said parallel lines intersect. I said that every line from one set of parallel lines will intersect every line from other set of parallel lines at the same angle.
Let me elaborate my whole point again.
Y = 2X+L  For each different value of L, this equation represents a line with slope 2. Thus the slope of each line is same, hence each line is parallel. L only defines the point at which the line intersects Yaxis (such a point is called intercept on Yaxis)
Y = XKL  For any value of K,L, this equation is a line with slope 1 (similar explanations as above)
Now, when you know the slope of 2 lines, you can find the angle between them using the formula : tan a = m1m2/(1+m1m2)



Senior Manager
Joined: 14 Jun 2007
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parsifal wrote: @anonymousegmat:
I never said parallel lines intersect. I said that every line from one set of parallel lines will intersect every line from other set of parallel lines at the same angle.
Let me elaborate my whole point again. Y = 2X+L  For each different value of L, this equation represents a line with slope 2. Thus the slope of each line is same, hence each line is parallel. L only defines the point at which the line intersects Yaxis (such a point is called intercept on Yaxis)
Y = XKL  For any value of K,L, this equation is a line with slope 1 (similar explanations as above)
Now, when you know the slope of 2 lines, you can find the angle between them using the formula : tan a = m1m2/(1+m1m2)
ok, but i thought triq wasn't on the gmat?



Manager
Joined: 21 May 2007
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I gave that formula only FYI, as a proof there does exist a mathematical formula to compute the angle.
GMAT wont test your trigonometry, otherwise the question would have been  find the angle....



Senior Manager
Joined: 14 Jun 2007
Posts: 392

parsifal wrote: I gave that formula only FYI, as a proof there does exist a mathematical formula to compute the angle. GMAT wont test your trigonometry, otherwise the question would have been  find the angle....
parsifal,
thanks. in my heart of hearts i KNEW there was some way to figure out the angle  but i approach DS questions within the context of 'algebra arithmetic gemoetry' only; if i can't answer it using basic math within the OG's official guidelines/math review then i choose insufficient. hypothetically speaking, higher mathmatics might be able to answer some DS questions based on statements given that algebra/geo/arithmetic can't.
i think this is just a bad example of a question, IMHO. if the gmat doesn't want you to learn trig they shouldn't ask a ? that utilizes it (i know they aren't asking me to calculate the angle  BUT they are presupposing a knowledge of trig with this question)



VP
Joined: 08 Jun 2005
Posts: 1135

anonymousegmat wrote: parsifal wrote: I gave that formula only FYI, as a proof there does exist a mathematical formula to compute the angle. GMAT wont test your trigonometry, otherwise the question would have been  find the angle.... parsifal, thanks. in my heart of hearts i KNEW there was some way to figure out the angle  but i approach DS questions within the context of 'algebra arithmetic gemoetry' only; if i can't answer it using basic math within the OG's official guidelines/math review then i choose insufficient. hypothetically speaking, higher mathmatics might be able to answer some DS questions based on statements given that algebra/geo/arithmetic can't. i think this is just a bad example of a question, IMHO. if the gmat doesn't want you to learn trig they shouldn't ask a ? that utilizes it (i know they aren't asking me to calculate the angle  BUT they are presupposing a knowledge of trig with this question)
I agree  does anyone know the source of this question ?



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Re: at what angle do lines y=Kx+L and x=y+KL intersect? I K=2 II
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24 Feb 2018, 23:54
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Re: at what angle do lines y=Kx+L and x=y+KL intersect? I K=2 II &nbs
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