PLEASE HELP ME WITH THIS MATH QUESTION WILL GIVE BRAINLIEST!!

1. what is the formula for finding the vertical distance between two points on a coordinate plane?

Is this a polynomial function? i need to know asap

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?