Question

The point in the \(xy\)-plane which is equidistant from the points \(A(2,0,3), B(0,3,2)\) and \(C(0,0,1)\) has the coordinates?

• A. \((3,2,0)\)
• B. \((2,3,0)\)
• C. \((2,0,8)\)
• D. \((0,3,1)\)

Hint:

Use distance formula and set equal distances to solve simultaneous equations for coordinates.

Answer 1

The Correct Option is A

Let point \(P(x,y,z)\) be equidistant from \(A, B, C\). \[ PA = PB \implies (x-2)^2 + y^2 + (z-3)^2 = x^2 + (y-3)^2 + (z-2)^2, \] \[ PB = PC \implies x^2 + (y-3)^2 + (z-2)^2 = x^2 + y^2 + (z-1)^2. \] From these, solve for \(x, y, z\), resulting in \[ (x,y,z) = (3,2,0). \]