Lines mn and pq are parallel. lines rs and tv intersect them. which statements are true about these lines? check all that apply.

the slope of line mn is .
the slope of line pq is undefined.
the slope of line rs is .
lines rs and tv are parallel.
line rs is perpendicular to both line mn and line pq.

The correct answer is:
RS is perpendicular to MN and PQ.

Explanation:
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.