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.

Question

Philoid · Accepted Answer

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,

XY =

For OC,

OC =

= …(1)

For AC,

AC =

=

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.