SOLUTION: There are eight points, each with integer coordinates that are 10 units from the origin. List the points.

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First the obvious choices
(10,0)
(0,10)
(-10,0)
(0,-10)
The next four are a little more challenging.


Think about the Pythagorean triples, particularly 3,4,5.
If we double them, we get 6,8,10, where 10 is the hypotenuse (or distance) that we're interested in.
(6,8)
(-6,8)
(8,6)
(-8,6)