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 perpendicular distance from a point \( P(a, b, c) \) to the y-axis is defined. The y-axis in 3D space consists of points where \( x = 0 \) and \( z = 0 \). Consequently, the distance from \( P(a, b, c) \) to the y-axis is equivalent to the distance of \( P \)'s projection onto the \( xz \)-plane from the origin.The general formula for the distance of a point \( (x, y, z) \) to the y-axis in three dimensions is:\[\text{Distance} = \sqrt{x^2 + z^2}.\]For the specific point \( P(a, b, c) \), its \( x \)-coordinate is \( a \) and its \( z \)-coordinate is \( c \). Substituting these values yields:\[\text{Distance from y-axis} = \sqrt{a^2 + c^2}.\] Thus, the correct answer is (C) \( \sqrt{a^2 + c^2} \).