# The point equidistant from points (0, 0), (2, 0) and (0, 2) is:A. (1, 2)B. (2, 1)C. (2, 2)D. (1, 1)

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 =

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.

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