Objective: Give the equation of a plane that crosses the axes at points equidistant from the origin.
How do I make sure that the points $A(1,2,-2)$, $B(-5,1,1)$, $C(4,-3,1)$ are equidistant from the origin or not? What method must I follow to solve this problem?
Best Answer
Hint:
The origin is $O(0,0,0)$.
Given two points: $P(x,y,z)$ and $Q(x',y',z')$ then the distance between those points, $d(P,Q)$, is:
$$d(P,Q) = \sqrt{(x-x')^2 + (y-y')^2 + (z-z')^2}$$
So what you want is $d(A,O) = d(B,O) = d(C,O)$.
Now, remember that a point on an axis has zeroes for two of it's coordinates.
(your $A$, $B$ and $C$ are not on any axis)