We can use the slopes of these lines to determine the answer. Slope is given by the formula m=.
Using the coordinates for M and N, we have: m=.
Since PQ is parallel to MN, its slope will be as well, since parallel lines have the same slope.
Using the coordinates for points T and V in the slope formula, we have m=.
This is not parallel to MN or PQ, since the slopes are not the same. We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.
Using the coordinates for R and S in the slope formula, we have m=. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.
