Hints/Answers:
The most direct points would be
found on the axes. (5, 0), (-5, 0), (0, 5), and (0, -5).
To find points that satisfy the
conditions of distance with integral values, think about the figure
that represents the set of all points a given distance from a
center. See an example of
this circle on graphing calculator.
There is a relationship between
the circle and the Pythagorean Theorem. This is illustrated below.
Notice that the length of one side
of the triangle is x and the other leg has length y. The point
on the circle is (x, y) and the distance to the point from the
center of the circle is
where
n is the radius of the circle.
For a demonstration of the circle
equation, click here.
By using the Pythagorean Theorem
eight additional integral points can be found.
