Q. 184.7( 7 Votes )

# Prove that the mi

Answer :

Consider a right angled ∆AOB, such that C is the mid–point of hypotenuse AB. We have O (0, 0)

Since A lies on y-axis, A (0, y)

and B lies on x-axis, B (x, 0)

Using mid–point formula, coordinates of C are Using distance formula,

AC = = = = = BC = = = = = We know that distance of a point P (x,y) from origin O (0, 0) is given as OP = OC = = = We can observe that OA = OB = OC.

C (mid–point of hypotenuse AB) is equidistant from all the three vertices of the right angled ∆AOB.

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