Provide an appropriate response.Show that the midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. [Hint: See the figure below. Show that = .]

Question

What will be an ideal response?

Answer 1

Verify that   = .

Cancel the 2's and square both sides:
² = ²  or
(a + b)?(a + b) = (a - b)?(a - b) or
a?a + 2a?b + b?b = a?a - 2a?b + b?b  [2a?b = 0 since a and b are orthogonal]
a?a + b?b = a?a + b?b Verified.
Thus, the midpoint is equidistant from all three vertices.