Creating Right Triangles!

Creation of this resource was inspired by this Open Middle problem submitted by Erick Lee. Using the digits 1-8 as coordinates of points A, B, and C at most one time each, position A, B, and C so they serve as vertices of a RIGHT TRIANGLE. How many possibilities exist here?

1.

List 3 ordered pairs (with no repeated coordinate digits) that make a right triangle. Then with these coordinates, prove algebraically that this triangle is indeed a right triangle.

2.

List a different set of 3 ordered pairs (with no repeated coordinate digits) that make a right triangle. Then with these coordinates, prove algebraically that this triangle is indeed a right triangle.

ADDED CHALLENGE: Same problem as above, but this time coordinates are integers ranging 1-6 instead!