Show that three points determine a right triangle: a (-1,2); b (4,-3); c (1,3).

Our strategy will be to use the definition of distance to get the lengths of the 3 sides ab, bc, ca of the triangle. Then we can use these lengths to see if they satisfy the Pythagorean Theorem.

First determine the 3 distances:

The longest side is ab. If this is the hypotenuse of a right triangle, the Pythagorean Theorem should be satisfied:

,

and it is.

Test Problem: Show that three points determine a right triangle: a (-2,4); b (1,-2); c (3,-1).