Creating Right Triangles 2

Directions: Using only the whole numbers 1 through 8 (without repeating any number), fill in the coordinates to create the vertices of a right triangle: A(__, __), B(__, __), C(__, __)

Extension: Try to do this using only the whole numbers 1 through 6.



What are the properties of a right triangle?
Which lattice points can be used to create the triangle? Which lattice points can not be used?



Using the whole numbers 1 to 8 there are a number of right triangles that can be created. Here are a few:

For each of the triangles above, an additional right triangle can be created by swapping the x and y coordinates (the reflection about line y=x).

Using the whole number 1 to 6 there are less possibilities. Here is one:
and its reflection about the line y=x

Source: Erick Lee

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