Answer:
(0,0), (-1,1), (-1,3), (0,4), (2,4), (3,3), (3,1), (2,0)
Explanation:
Assuming that "root5" is the square root of five (√5)...
Method A:
We know by the Pythagorean Theorem that the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse. The only way to have leg lengths that are integers in this case, is for one leg to equal 1 and the other leg to equal 2 (1² + 2² = 5). So if we start at the point (1,2) and form right triangles with these leg lengths, we will find what is requested. (see the blue triangles in the figure)
Method B:
Use the given information to write the equation of a circle with center at (1,2) and radius of √5: (x-1)²+(y-2)²=5.
If we graph this circle, we actually see that there are 8 points with integer coordinates on the circle - the first of which is at the origin: (0,0).
(see the green circle in the figure)