Question

In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.

Answer 1

We have a right angled triangle, right angled at O. Co-ordinates are B (0,2b); A (2a, 0) and C (0, 0).

We have to prove that mid-point C of hypotenuse AB is equidistant from the vertices.

In general to find the mid-point of two pointsand we use section formula as,

So co-ordinates of C is,

In general, the distance between A and B is given by,

So,

Hence, mid−point C of hypotenuse AB is equidistant from the vertices.