if the direction between two point P (1,2) and M(5, y) is 5 find the value of y using the formula please urgent 100point fast answer please no spam answer please

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?

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.

Which of the following is an example of a rational number? a. π b. √ 9 c. √ 8 d. 3.8362319