Learning Resources

Investigation 6: The Equation of a Circle

Step B

To get a point on the circle with "integral" coordinates you have to think of the Pythagorean theorem and determine what integral values of x and y will make the theorem true. For example, in the triangle below what are possibilities for the sides x and y?
                          

We know from the Pythagorean theorem that x² + y² = 10^2.  Consider some integral values that don't work:

                  2 and 3 don't work because  2² + 3² = 4 + 9 = 13  ¹10²
                  5 and 9 don't work because  5² + 9² = 25 + 81 = 106  ¹10²

So what would work? Use guess and test until you find a pair of numbers that will work.

It can be shown that 6 and 8 work because  6² + 8² = 36 + 64 = 100 = 10². So you could use these coordinates for Step B.