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?
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?
Show Hint
Use distance formula and set equal distances to solve simultaneous equations for coordinates.
Updated On: Mar 18, 2026
- \((3,2,0)\)
- \((2,3,0)\)
- \((2,0,8)\)
- \((0,3,1)\)
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The Correct Option is A
Solution and Explanation
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
\[
(x,y,z) = (3,2,0).
\]
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