ruchisharma wrote:In the xy-plane, line K passes through the point (1,1) and line M passes through the point (1,-1). Are lines K and M perpendicular to each other?

1.) Lines K and M intersect at the point (1,-1).
2.) Line K intersects the x-axis at the point (1,0).

Throuugh a single point any number of lines can be drawn
Through two points only one line can be drawn.
1,0
1.) Lines K and M intersect at the point (1,-1).
This means that K passes thru (1,1) and (1,-1). hence we know line K
but for Line M, we know only one point. So we cant say if the line is perpendicular or not.
INSUFF

2.) Line K intersects the x-axis at the point (1,0).
Now, we know that K passes thru (1,1) and (1,0)
This means that K is parallel to y axis. This means K is passing thru (1,-1)(1,0)(1,1)(1,2)..etc
Hence Line M is passing thru (1,-1). But we do not know, at what angle it is passing.
Hence INSUFF

Combining:
Even now, we do not know the slope or eqtn of M
Henc eINSUFF

pick E.

whats OA?

E it is

For 2 lines to be Perpendicular the product of their slopes must be -1 , i.e. m1xm2 = -1.

frm 1 - We get where line K and M meet which is the same point as M (1,-1) , so from this data only the slope of K can be found but not both.

NOT suff.

from 2- Here as well K intersects with X axis at some point (1,0) which will give the slope of K only. thus nothing can be said about line K and M being Perpendicular.

Not Suff

combining both 1 & 2 - we get only slope of line K. So again.

Not Suff

So the answer IMO is E