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The point on the x-axis equidistant from (1, 2, 3) and (3, 2, −1) is
A(−1, 0, 0)
B(0, 0, 0)
C(1, 0, 0)
D(2, 0, 0)
Answer & Solution
Correct answer: B. (0, 0, 0)
Let the point be (a, 0, 0). Distance² to (1,2,3) = (a−1)² + 4 + 9 = a² − 2a + 14. Distance² to (3,2,−1) = (a−3)² + 4 + 1 = a² − 6a + 14. Setting equal: −2a = −6a ⇒ a = 0. So the point is the origin.
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