two lines are perpendicular only if product of thier slopes = -1

to find out slopes you need at least another point for each line

from stmt 1 only slope for line k can be determined (insuf)

from stmt 2 only slope for like k can be determined

together , if we plot these points you will see there can be infinite line m going thru point (1,-1) which may or may not be perpendicular to line k.
hence E.

can someone give a detailed explain. I do not know anything about analytical geometry. I do think many of us don't know as well.

If you tried to do this visually you would need to draw the 2 lines above on an x-y graph. Since the question stem gives us a point for each line k and m we need either another distinct-point (for each) or the slope (for each). So rewording the question "can we draw the 2 lines on an x-y plot"

1) gives us another point but notice that this point same point given for m. This allows us to draw line k but not m. --> Insuff

2) This gives us a point for line k. SO again we can draw k but not m. --> insuff

Combined - for both we can draw k but not m --> insuff

E

perfectstranger wrote:can someone give a detailed explain. I do not know anything about analytical geometry. I do think many of us don't know as well.

remember basic thing that 2 lines will be perpendicular if the product of slopes of both lines is -1.

Since we 2 points for line k we can find out its slope but we do not have any information about line m except that its passes thru point(1,-1).

We can determine its and hence unable to answer with the give choices.
So, answer is 'E'