DS - Coordinate Geometry

[oks]

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 intersect the x-axis at the point (1, 0)

Answ: E.

I thought it could be C.

Any ideas?

Thanks!!!

[alescau]

each line needs two data points to be defines.
(1) tells us something about k, not m.
(2) tells us about k.

we have three points for k, but still one for m. thus we can not tell what m looks like.

thus, E.

[csandeepreddy]

Its easier if you draw the graph. It clearly shows what alescau is trying to say.

[tendays2go]

choice(i) =>
line k: x=1 (line passing both(1,1) and (1,-1))
but tells nothing about line m as there can be infinite lines passing through one point, in this case (1, -1)

so can't say if the two lines are 90 deg to each other or not.

choice(ii) =>
similarly, line k: x=1 (line passing both(1,1) and (1,0))
here again there's no info on line m apart from the info in question which is insufficient as seen previously.

combining these two choices also doesn't give any eqn for line m, so it has to be (E)