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# If L and K are lines in xy- plane, is the product of the

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Manager
Joined: 23 Jan 2008
Posts: 104
If L and K are lines in xy- plane, is the product of the  [#permalink]

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31 Jan 2008, 18:24
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88% (01:14) correct 12% (01:21) wrong based on 247 sessions

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If L and K are lines in xy- plane, is the product of the slope of L and K equal to -1?

(1) Line L passes through the origin and the point (1,2).
(2) Line K has x-intercept 4 and y-intercept 2.
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Posts: 52297
Re: If l and K are lines in xy- plane, is the product of the  [#permalink]

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16 Jul 2012, 04:42
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We don't need to calculate anything to answer this question.

If L and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

The product of two lines equal to -1 if these lines are perpendicular to each other. So, the question basically asks whether L and K are perpendicular to each other.

Now, if we knew the equations of each line we would be able to answer the question. What do we need to find equation of a line? Since a line is defined by two points, then if we knew any two points of a line then we could get its equatiom

(1) Line L passes through the origin and the point (1,2). We have two points of line L: (0, 0) and (1, 2). So, we can get the equation of line L, though we know nothing about line K. Not sufficient.

(2) Line K has x-intercept 4 and y-intercept 2. We have two points of line K: (4, 0) and (0, 2). So, we can get the equation of line K, though we know nothing about line L. Not sufficient.

(1)+(2) We know both equation, hence we can answer whether the lines are perpendicular to each other. Sufficient.

venmic wrote:
Can anyone give a better explanation on this one please

Hovv does K have a slope of -1/2 out of novvhere at all

Given two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ on a line, the slope $$m$$ of the line is:

$$m=\frac{y_2-y_1}{x_2-x_1}$$.

Since x-intercept of line K is 4, then it passes through point (4, 0) and since y-intercept of line K is 2, the it passes through point (0, 2). Hence it's slope is $$m=\frac{2-0}{0-4}=-\frac{1}{2}$$.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

Hope it helps.
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Joined: 29 Mar 2007
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Re: DS - if l and k  [#permalink]

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31 Jan 2008, 20:15
blog wrote:
If l and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

1. Line l passes through the origin and the point (1,2).
2. Line K has x-intercept 4 and y-intercept 2.

C

1: we dont know anything about the other line but we can find the slope of line l = 2

2: again we dont know the other line's slope but k's is -1/2

Together 2*-1/2= -1

But you could just realize that 1 and 2 are suff together b/c we know the slopes we are going to get a YES OR A NO NOT BOTH. so u could save some time.
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Re: DS - if l and k  [#permalink]

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01 Feb 2008, 09:55
blog wrote:
GMATBLACKBELT wrote:
blog wrote:
If l and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

1. Line l passes through the origin and the point (1,2).
2. Line K has x-intercept 4 and y-intercept 2.

C

1: we dont know anything about the other line but we can find the slope of line l = 2

2: again we dont know the other line's slope but k's is -1/2

Together 2*-1/2= -1

But you could just realize that 1 and 2 are suff together b/c we know the slopes we are going to get a YES OR A NO NOT BOTH. so u could save some time.

how come u get k's = -1/2 in 2 ?

(4,0) and (0,2) --> (0-2)/(4-0) --> -2/4 --> -1/2

Formula for slope is (y1-y2)/(x1-x2)
Manager
Joined: 20 Dec 2004
Posts: 246
Re: DS - if l and k  [#permalink]

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02 Feb 2008, 13:41
>> Line K has x-intercept 4 and y-intercept 2.

Its not clear if the x-intercept is going to be a (4,0). All it said is that x-intercept is 4 and y-intercept is 2. Even a coordinate of (-4,0) equals an x-intercept of 4.

So the x coordinates can be (4,0) or (-4,0) and y coordinates can be (0,2) or (0,-2)

So there are two possible lines that are perpendicular and the other 2 are not.

So in my opinion E.

What is the OA ?
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Manager
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Posts: 246
Re: DS - if l and k  [#permalink]

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02 Feb 2008, 16:44
my mistake if 1) is true then 2) will have a specific set of coordinates.

C is correct...

Need to be more cautious.
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Manager
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Re: DS - if l and k  [#permalink]

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02 Feb 2008, 20:51
neelesh wrote:
my mistake if 1) is true then 2) will have a specific set of coordinates.

C is correct...

Need to be more cautious.

what do u mean by 2 has to have a specific set of cordinates .. form what i see i agree to your earlier assumption ...when u say line k has 4 as x cordinate and 2 as y cordinate u can very well say that it is a cordinate of the same point (4,2) then u cannot say anything about K's slope as it just passes through one point .. please explain as i still feel it should be E
Manager
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Posts: 104
Re: If l and K are lines in xy- plane, is the product of the  [#permalink]

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15 Jul 2012, 22:10
Can anyone give a better explanation on this one please

Hovv does K have a slope of -1/2 out of novvhere at all

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Re: If L and K are lines in xy- plane, is the product of the  [#permalink]

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20 Oct 2012, 13:46
1
read 2) carefully - line K has an x-intercept of 4 (meaning it hits the x axis at 4--- so the point would therefore be 4,0) and y-intercept of 2 (meaning it hits the y axis at 2---so the point would therefore be 0,2). So we now have (4,0) and (0,2) as our two points for line K and we can plug it into our slope formula of y2 - y1/x2 - x1 --> y2 = 2 y1 = 0 x2 - 0 y1 = 4 --> 2-0/0-4 ---> 2/-4 = -1/2.

Hope this helps!
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Joined: 11 Sep 2015
Posts: 3344
Re: If L and K are lines in xy- plane, is the product of the  [#permalink]

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30 Apr 2018, 09:23
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Top Contributor
blog wrote:
If L and K are lines in xy- plane, is the product of the slope of L and K equal to -1?

(1) Line L passes through the origin and the point (1,2).
(2) Line K has x-intercept 4 and y-intercept 2.

IMPORTANT: For geometry and coordinate plane Data Sufficiency questions, we are often checking to see whether the statements "LOCK" a particular line, angle, length, or shape into having just one possible position or measurement. This concept is discussed in much greater detail in the video below.

Target question: Is the product of the slopes of l and k equal to -1?

IMPORTANT: The product of the slopes will equal -1 if the lines are perpendicular to each other (unless the two lines are horizontal and vertical, in which case the product will equal zero). This allows us to REPHRASE the target question as...

REPHRASED target question: Are the two lines perpendicular to each other?

Statement 1: Line l passes through the origin and the point (1, 2)
NOTICE that statement 1 LOCKS line l into ONE AND ONLY ONE line.
That said, we have no information about line k, so we cannot determine whether the two lines are perpendicular to each other.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Line k has x-intercept 4 and y-intercept 2.
NOTICE that statement 1 LOCKS line k into ONE AND ONLY ONE line.
That said, we have no information about line l, so we cannot determine whether the two lines are perpendicular to each other.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 LOCKS in the shape of line l
Statement 2 LOCKS in the shape of line k
So, we COULD very well determine whether or not the two lines are perpendicular to each other
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEO

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Re: If L and K are lines in xy- plane, is the product of the &nbs [#permalink] 30 Apr 2018, 09:23
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