The distance between the y-axis and the point (1, 2, 3) is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\sqrt{10}\) units
The foot of the perpendicular from P(1, 2, 3) to the y-axis is the point of the y-axis with the same y-coordinate, (0, 2, 0). So the distance is
\( \sqrt{(1-0)^2 + (2-2)^2 + (3-0)^2} = \sqrt{1 + 9} = \sqrt{10} \)
In general, the distance of (x, y, z) from the y-axis is \(\sqrt{x^2 + z^2}\): the y-coordinate plays no part.
Why the other options are incorrect
Option (1) 2 units — Incorrect. 2 is the y-coordinate, which is the distance from the xz-plane, not from the y-axis.
Option (3) \(\sqrt{13}\) units — Incorrect. \(\sqrt{2^2 + 3^2} = \sqrt{13}\) is the distance from the x-axis.
Option (4) \(\sqrt{5}\) units — Incorrect. \(\sqrt{1^2 + 2^2} = \sqrt{5}\) is the distance from the z-axis.