In the rectangular coordinate system, lines m and n cross at

[poojakrishnamurthy1]

Hi,

Got this question in CAT 5.

In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n?

(1) m has a slope of -1 and n passes through the point (-a, -a).

(2) If the slope of m is x and the slope of n is y, then -xy = 1.

Doubt-
The Original Answer is D but my answer is B. The explanation given by Manhattan is -

(1) SUFFICIENT: Because we know the lines pass through the origin, we can figure out if the slopes are negative reciprocals of each other. The slope of m is -1 so if the slope of n is 1 (-1/-1) then we know the lines are perpendicular and the angle between them is 90°. Because we know two points for line n, (0, 0) and (-a, -a), we can calculate the slope:

0 - (-a)
--------- = 1
0 - (-a)


Thus the lines are perpendicular and the angle between them is 90°.

However, choice A fails to take into account that a=0, in which case (a,a) and (-a,-a) equal (0,0) and so lines M and N may NOT necessarily be perpendicular.

I ask the Manhattan GMAT CAT Quant faculty to please amend the problem and mention that a is a non-zero number.

[Guest]

Thats very insightful and displays great clarity of purpose on your part. Although I think its clear that if it has already been mentioned that the lines pass through origin. And the new points are additional point the lines pass through. Dont think of a as a variable, think of it as a constant. This is a regular convention in Coordinate geometry.

[shaji]

a can't be 0;0/0 is indeterminate. Further; -0 is +0 are nonexistant.

[RonPurewal]

the original poster is correct: if it's not explicitly stated that a is nonzero, statement (1) allows for the possibility that (-a, -a) = (0, 0), meaning that line n can go in whatever direction its little heart desires.

we will fix this problem.
thank you.

[JK]

GOOD MAN RON, GOOD MAN

[nathanhbaldwin]

Could anybody help me understand why we assume the line has to follow the y=mx+b pattern? I thought the answer was B because in A, the line could not be straight. Thanks for the help.

[tim]

every line is straight, and every line can be expressed in terms of y=mx+b. these are just things that are fundamentally true of lines..