Explanation:
then let's change that. you don't want to stay a dumdum, right ?
midpoint. what does that mean ? it is the point exactly in the middle between 2 other points.
what does that mean to be in the middle between 2 other things ?
well, it means that the distance is the same to both other things. otherwise it would not be the middle.
therefore,
4.
QS = 56 ft
exactly the same distance as PQ.
PS = PQ + QS
because Q is the point in the middle between P and S.
it is really that simple.
5.
the line segment PQ is bisected (cut in half) by the line segment MN at point R.
so, we know what the intersection of PQ and MN did to PQ (cut PQ in half). but this does not tell us what it did to MN. it could be also one of the ends of MN that cut PQ in half. we simply don't know.
therefore, we cannot say anything about the midpoint of MN.
and therefore the first 2 answer options are not generally correct. they COULD be correct, but they could be also wrong. therefore they are mathematically and logically not a true statement per se. for that the statement needs to be true unconditionally = in all possible cases.
R is the midpoint of PQ. yes, correct. that's what is meant by being bisected or cut in half at that point.
since the 3rd answer option is correct, the 4th answer option (none of these) is incorrect.