Help :D i don’t understand number 8 or 9

What is the distance between the points 4,10 and -3,-14 on the coordinate plane

In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision. (1,-1), (2,0.5), (5,1.5), (8,2)

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?