M03 #15

Question

If two lines have slopes  m  and  n  , respectively, are they perpendicular?

1.  m*n=-1 
2.  m=-n

I have an issue in OE when explaining the statement 2. From OE shown below one can still answer the question that whether m & n are perpendicular.

I think in OE there should be two examples. First an example of two lines  y= x+10  &  y=-x+10 , here you can see that the lines are parallel as the product of their slope is  -1 . In second example we can quote  y=10x  &  y=-10x . Now its make more sense that statement 2 is insufficient.

OE:
Statement (2) by itself is insufficient. We only know that the lines have reciprocal slopes. For example line  y=10x  and  y=-10x  , are mirror reflections of each other on the x axis, but not perpendicular.

iPinnacle · Answer

Statement-1: 
We know that if two lines are perpendicular to each other, their slopes will be negative reciprocal to each other.
So here m*n= -1 => m = -1/n (Hence SUFFICIENT)

Statement-2: 
m=-n 
They can be negative reciprocal for some numbes(like 1) but not for others.(Hence NOT SUFFICIENT)

Ans : A

OA?

flash · Answer

Shouldn't statement 2 be sufficient because the lines are never going to be perpendicular.??

tom99green · Answer

@flash
Nope . see the first reply.
eg: m=1 , n = -1 . 
That could be one of the answers. So not sufficient with stmt 2.

flash · Answer

aaah...got ya. tks

M03 #15

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