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Line L passes

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Line L passes [#permalink] New post 19 May 2017, 02:08
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Question Stats:

76% (00:43) correct 23% (00:26) wrong based on 39 sessions


Line l passes through \((- \sqrt{2}, \sqrt{3} )\) and \(( \sqrt{2}, -\sqrt{3} )\). Line M is perpendicular to line l

Quantity A
Quantity B
The slope of l
The slope of M


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Director
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Re: Line L passes [#permalink] New post 09 Oct 2017, 08:22
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Given that line m is perpendicular to line l and the slope of a perpendicular line is the opposite reciprocal of the other.

Than it is enough to notice that line l slope is some negative stuff divided by some positive stuff, thus it is negative. Line m slope is then positive.

Quantity B is greater and B is the answer!
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Re: Line L passes [#permalink] New post 09 Oct 2017, 11:13
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Carcass wrote:


Line l passes through \((- \sqrt{2}, \sqrt{3} )\) and \(( \sqrt{2}, -\sqrt{3} )\). Line M is perpendicular to line l

Quantity A
Quantity B
The slope of l
The slope of M


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Detailed explanation

Now we know slope of line\(m = \frac{(y2 - y1 )}{(x2 -x1)}\)

Therefore the slope of line\(l= \frac{(y2 - y1 )}{(x2 -x1)}\) [ where y2 = \(-\sqrt{3}\), y1 =\(\sqrt{3}\)and x2 = \(\sqrt{2}\) and x1 =\(-\sqrt{2}\) ]

\(=(-\sqrt{3}-\sqrt{3})/(\sqrt{2}+\sqrt{2})\)

\(= -\sqrt{3}/\sqrt{2}\)

Now slope of line \(M = \sqrt{2}/\sqrt{3}\) (Since the slope M is perpendicular to line l and we know the slope is negative reciprocal)

Hence option B is greater since it is positive value
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Re: Line L passes [#permalink] New post 29 Sep 2018, 11:26
I picked B
Re: Line L passes   [#permalink] 29 Sep 2018, 11:26
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