### Math Notes

Subjects

#### Analytic Geometry Solutions

##### Topics || Problems

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

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.