Question

Line $l$, line m, and point P lie in a plane such that $l$|| $m$ and $P$ is between $l$ and $m$. If line $t$ in the same plane passes through point $P$, which of the following could be true?
I.$t$ intersects $l$ but not $m$.
II. $t$ intersects both $l$ and m.
III. $t$ does not intersect either $l$ or $m$.

• A. I only
• B. II only
• C. III only
• D. I and II
• E. II and III

Answer 1

The correct option is E II and III

Given that $2$ parallel lines, $l$ and $m$ lie in the same plane as point $P$.

Another line $t$ is in the same plane.

This line either intersects both or none.

If it is parallel two the first 2 lines, then it never intersects.

If it is not parallel, then it intersects both. There is no way possible that it intersects any one line.

Hence, Option E.