In Fig. 14.40, a right triangle BOA is given. C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices 0, A and B.
Given that ∆BOA is right angled triangle
By midpoint formula,
x = , y =
For midpoint C on AB,
x =, y =
∴ x = a and y = b
∴ Coordinates of C are (a, b)
It is given that C is the midpoint of AB.
By distance formula,
As C is midpoint, AC = CB. …(2)
Hence from 1 and 2, we say that is point C is equidistant from the vertices 0, A and B.
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