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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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Senior Manager
Joined: 14 Jun 2007
Posts: 392
at what angle do lines y=Kx+L and x=y+KL intersect? I K=2 II  [#permalink]

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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

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Manager
Joined: 21 May 2007
Posts: 117

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23 Jun 2007, 11:11
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

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23 Jun 2007, 11:47
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=KL-x = y=x-KL

y=x-KL has slope of 1

therefore they aren neither parallel nor perpendicular; so how do we derive the angle of intersection?

from
VP
Joined: 08 Jun 2005
Posts: 1135

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Updated on: 23 Jun 2007, 23:26
1
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 = X-KL

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 = X-KL

we can't find the slopes (K,1) so:

insufficient

Originally posted by KillerSquirrel on 23 Jun 2007, 13:38.
Last edited by KillerSquirrel on 23 Jun 2007, 23:26, edited 2 times in total.
Manager
Joined: 21 May 2007
Posts: 117

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23 Jun 2007, 15:25
@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 Y-axis (such a point is called intercept on Y-axis)

Y = X-KL - 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 = |m1-m2|/(1+m1m2)
Senior Manager
Joined: 14 Jun 2007
Posts: 392

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23 Jun 2007, 15:39
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 Y-axis (such a point is called intercept on Y-axis)

Y = X-KL - 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 = |m1-m2|/(1+m1m2)

ok, but i thought triq wasn't on the gmat?
Manager
Joined: 21 May 2007
Posts: 117

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23 Jun 2007, 15:45
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

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24 Jun 2007, 08:41
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

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24 Jun 2007, 12:09
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  [#permalink]

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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 [#permalink] 24 Feb 2018, 23:54
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