Line K passes through point (1,1) and M passes through (1,-1).

Draw those two points and you will realise that one is in 1st quadrant and other in 4th. This is what the question stem tells you. And the question is are the two lines perpendicular.

Statement 1:
Tells us that lines intersect at point 1,-1.
If you drawn the above two points and now you join (1,1) and (1,-1), which are the two points of line K, you will know the line K.
This line K is parallel to Y axis.
However, all we know about line M is that it passes through 1,-1. And there can be infinite such lines. We cant conclude whether the two lines are perpendicular.

So, INSUFFICIENT.

Statement 2:
This tells us that Line K passes through 1,0. Join 1,1 and 1,0. Once again you will get a line parallel to Y axis. Again if you extend this line you will realise that it will cross point 1,-1. But the situation is similar to Statement 1.

So, INSUFFICIENT

Combining the two statements only gives us line k again and we still don't know how Line m is. This we got from both statements separately as well anyway.

Also, any two perpendicular lines will have the product of their slopes as -1.
So you can also take the question as asking 'is the product of their slopes -1 ?'

Now, we can find out the slope of a line if we know two points it passes through.

The question itself gives us one point for each line.

Statement 1 gives us another point for line k but not m
Statement 2 again gives us another point for line k but not m
Combining them, we have three points for k but only one for m.