Question

Find the coordinates of the point which is equidistant from the three vertices A (\[2x, 0) O (0, 0) \text{ and }  B(0, 2y) of ∆\]  AOB .

 

 

 

Answer 1

It is known that, in a right angled triangle midpoint of the hypotenuse is equidistant from ots vertices.
Suppose D be the midpoint of the hypotenuse AB.
The coordinates of D are \[\left( \frac{2x + 0}{2}, \frac{0 + 2y}{2} \right) = \left( x, y \right)\] .