Mathematics Notes - Analytic Geometry Problems and Solutions

Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

$proving right triangles$

To prove this one, we need to show that p = d.

$ a^2 +b^2 = c^2$

$ a^2 +b^2 = (2p)^2$

$ a^2 +b^2 = 4p^2$

$ (\frac{b}{2})^2+(\frac{a}{2})^2 = d^2$

$ \frac{a^2}{4} + \frac{b^2}{4} = d^2 $

$ a^2 + b^2 = 4d^2 $

$ 4p^2 = 4d^2$

$ p = d$

Therefore since p = d, the statement is true.