Coordinate plane problem?

Question

I need to answer this question. There's a new problem each week that we have to answer, and this has NOthing to do with the geometry that we're studying, so...

Find the coordinates of all points in the Cartesian plane (I think that's just a regular coordinate plane) that are equidistant from the x-axis, the y-axis, and the point (2,1).

If you could provide and answer and explanation, that would be great.
Thank you so much!
I'll choose best answer ASAP

Answer 1

(1,1)
(5,5)

let such a point be (x,y)
since it is equidistant from the x and y axes, y=x
(Or y= -x . However, points on this line will always be closer to an axis than to the point (2,1), so we ignore them.)

The distance from (x,x) to (2,1) is
√[(x-2)^2 + (x-1)^2]
= √(2x^2 - 6x + 5)
and the distance from (x,x) to each axis = x ,
so x = √(2x^2 - 6x + 5)
x^2 = 2x^2 - 6x + 5
x^2 - 6x + 5 = 0
(x-1)(x-5) = 0
x = 1 or x = 5

Answer 2

Draw circles, then you get it.