Choice
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you use neither when none of them are correct and you use either when both can be correct. :) 2nd Answer: "Either" goes with "or", as in, "Either you or I will go". That means one or the other. "Neither" goes with "nor", as in, "Neither you nor I will go". That means that nobody will go.
You cannot. At least, not one point. If the distance between the two given points is b, and the area of the triangle is A, then let h = 2A/b Then draw two lines parallel to the line formed by the two given points - one above and one below, each of these lines being at a distance h from the first line. Any point on either of these two lines will meet your requirements.
Only one
Knowing the length of the hypotenuse doesn't tell you the length of either adjacent side. You also need to know at least one other piece of information, like the other side, or an angle.
Playfair Axiom