The point equidistant from points (0, 0), (2, 0) and (0, 2) is:

We have A → (0, 0)

B → (2, 0)

C → (0, 2)

Let D (x,y) be equidistant from A, B and C.

We know that distance of a point A (x,y) from origin O (0, 0) is given as OA =

∴ AD = …(i)

Using the distance formula,

BD =

=

= –––(ii)

CD =

= –––(iii)

Since D is equidistant from A, B and C

Equating eq (i) and (ii)

Squaring both sides

4y – 4 = 0

y = 1

Equating eq (i) and (iii)

Squaring both sides

4x – 4 = 0

x = 1

The required point is D (1, 1).

∴ The correct option is D.