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.

Hint

Hint

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?

Answer

Answer

Using the whole numbers 1 to 8 there are a number of right triangles that can be created. Here are a few:
(1,3)(2,6)(8,4)
(1,7)(2,8)(4,6)
(1,7)(2,8)(6,4)
(1,6)(3,8)(4,7)

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:
(1,5)(3,2)(6,4)
and its reflection about the line y=x
(5,1)(2,3)(4,6)

Source: Erick Lee

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