Question

What point is equidistant from `(0, 0)`, `(3, 0)` and `(6, 0)` ?

Answer 1

Ans: (3, 0)

Explanation:

Call M (x, y) the point that is equidistant from A (0, 0), and (6, 0).
x-coordinate of M --> x = (6 - 0)/2 = 3
Coordinates of M (3, 0)
Answer: Point M (3, 0).

Answer 2

There is no such point. These three points are colinear.

Explanation:

All of the points `(0, 0)`, `(3, 0)` and `(6, 0)` lie on the `x` axis.

The points which are equidistant from `(0, 0)` and `(3, 0)` all lie on the line `x = 3/2`.

The points which are equidistant from `(3, 0)` and `(6, 0)` all lie on the line `x = 9/2`.

These parallel lines do not meet: you cannot satisfy both equations at the same time. So there is no point which is equidistant from all three given points.