Question

is $overleftrightarrow{pr}perpoverleftrightarrow{np}$? explain

no; the two lines do not intersect.

no, because $overleftrightarrow{pq}$ is marked perpendicular to $overleftrightarrow{np}$, $overleftrightarrow{pr}$ cannot also be perpendicular to $overleftrightarrow{np}$

yes, the two lines are marked perpendicular.

yes, because $overleftrightarrow{pq}$ is marked perpendicular to $overleftrightarrow{np}$, $overleftrightarrow{pr}$ is also perpendicular to $overleftrightarrow{np}$

Explanation:

Step1: Check intersection

Perpendicular lines must intersect. $\overleftrightarrow{PR}$ and $\overleftrightarrow{NP}$ intersect at some point (as they are in the same plane and not parallel). But the key is the relationship with $\overleftrightarrow{PQ}$.

Step2: Use perpendicular property

If a line ($\overleftrightarrow{PQ}$) is perpendicular to a given line ($\overleftrightarrow{NP}$), another line ($\overleftrightarrow{PR}$) which is not the same as the perpendicular - marked line ($\overleftrightarrow{PQ}$) cannot be perpendicular to $\overleftrightarrow{NP}$ at the same time (in a plane, through a point on a line, there is exactly one line perpendicular to the given line). Since $\overleftrightarrow{PQ}\perp\overleftrightarrow{NP}$, $\overleftrightarrow{PR}$ is not perpendicular to $\overleftrightarrow{NP}$.

Answer:

no, Because $\overleftrightarrow{PQ}$ is marked perpendicular to $\overleftrightarrow{NP}$, $\overleftrightarrow{PR}$ cannot also be perpendicular to $\overleftrightarrow{NP}$