Prove that the median to the hypotenuse of a right triangle is half the hypotenuse. Proof: By the Distance Formula, MN = _. Therefore, OP=1/2 MN.

Option (A).

Step-by-step explanation:

From the figure attached,

ΔMON is a right triangle and coordinates of the points M and N are M(0, 2b) and N(2a, 0).

Coordinates of midpoint P →

                                            → (a, b)

From the formula of the distance between two points,

d =

MN =

      =

      = 2

Similarly, OP =

                     =

Therefore, OP =

and MN = = 2

Option (a) is the answer.