Question

The distance of the point \( P(a, b, c) \) from the y-axis is:

• A. \( b \)
• B. \( b^2 \)
• C. \( \sqrt{a^2 + c^2} \)
• D. \( a^2 + c^2 \)
• E.

Hint:

To find the distance of a point from an axis, exclude the coordinate corresponding to that axis and use the Pythagorean theorem to calculate the distance in the remaining plane.

Answer 1

The Correct Option is C

The distance of a point \( P(a, b, c) \) from the y-axis is the perpendicular distance from the point to the y-axis. The y-axis in three-dimensional space has coordinates where \( x = 0 \) and \( z = 0 \). Thus, the distance from \( P(a, b, c) \) to the y-axis is determined by the projection of \( P \) onto the \( xz \)-plane. The distance formula in three dimensions for a point \( (x, y, z) \) to the y-axis is given by: \[ \text{Distance} = \sqrt{x^2 + z^2}. \] For \( P(a, b, c) \), the \( x \)-coordinate is \( a \) and the \( z \)-coordinate is \( c \). Therefore: \[ \text{Distance from y-axis} = \sqrt{a^2 + c^2}. \] Hence, the correct answer is (C) \( \sqrt{a^2 + c^2} \).