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bit tricky slope

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Source: — Data Sufficiency |
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by goyalsau » Mon Dec 20, 2010 3:41 am
Night reader wrote:Is the slope of line l positive?

(1) (0,5) is the intersection point of line l with the y axis

(2) Line l is perpendicular to line y = 5x + 9
When two lines are perpendicular to each other, They share a relation... M1 * M2 = -1

Or we can say that Slope of Lines must be negative reciprocal to each other.

We have the slope of one line , as 5 , so the slope of the line that is perpendicular to that must be -1/5

Hence Sufficient.

option B
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by fskilnik@GMATH » Mon Dec 20, 2010 4:44 am
goyalsau wrote: When two lines are perpendicular to each other, They share a relation... M1 * M2 = -1

Or we can say that Slope of Lines must be negative reciprocal to each other.
Hi there!

Your argument is excellent, goyalsau, but let us make it absolutely perfect:

Two (planar) lines are perpendicular to each other if and only if:

(i) One of them is horizontal (slope zero) and the other is vertical (slope is not defined)

OR

(ii) their product is -1.

Please note that (ii) IMPLICITLY assumes that both slopes EXIST and it EXPLICITLY guarantees that NONE of them is zero (otherwise their product would be zero).

Regards,
Fabio.

P.S.: I hope you don´t mind this small correction... as far as understanding concepts is concerned, I guess every small observation matters! :)
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Night reader » Mon Dec 20, 2010 5:13 am
thanks, Fabio. I answered this question correctly by drawing sample lines and inferring that with one equation given we may either confirm or cancel that two lines are perpendicular. Goyalsau and you have shed light on this question concept-wise. BTW, is there any theorem to prove the relationship of perpendicular lines in a plane. I would like to cement this relationship in my mind.
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by fskilnik@GMATH » Mon Dec 20, 2010 5:20 am
Night reader wrote:thanks, Fabio. I answered this question correctly by drawing sample lines and inferring that with one equation given we may either confirm or cancel that two lines are perpendicular. Goyalsau and you have shed light on this question concept-wise. BTW, is there any theorem to prove the relationship of perpendicular lines in a plane. I would like to cement this relationship in my mind.
My pleasure, Night reader.

As far as the theorems you´ve asked are concerned, for GMAT-purposes I believe what I wrote is the only one you must know in terms of coordinate-Geometry perpendicularity.

Regards,
Fabio.
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by goyalsau » Mon Dec 20, 2010 7:27 am
fskilnik wrote:
(i) One of them is horizontal (slope zero) and the other is vertical (slope is not defined)
HI! Fabio , Thanks for reminding the slopes of horizontal and Vertical lines.
Slope of Horizontal line is Zero, Because change is Y Coordinates Is Zero.. ... When you divide Zero by any thing its zero.

Slope of Vertical line is undefined, Because Change is X Coordinates is Zero... When you divide any thing by Zero, it is undefined.
fskilnik wrote: (ii) their product is -1.
Then How can we say that product of Slopes of Perpendicular lines is -1, Because in case of X and Y axis there slope is Zero.....
fskilnik wrote: Please note that (ii) IMPLICITLY assumes that both slopes EXIST and it EXPLICITLY guarantees that NONE of them is zero (otherwise their product would be zero).

Regards,
Fabio.

P.S.: I hope you don´t mind this small correction... as far as understanding concepts is concerned, I guess every small observation matters! :)
Saurabh Goyal
[email protected]
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