Solve the problem.
-Find a formula for the distance from the point P(x, y, z) to the z-axis.
A) $\sqrt { z + y }$
B) $\sqrt { x + y }$
C) $\sqrt { \mathrm { z } ^ { 2 } + \mathrm { y } ^ { 2 } }$
D) $\sqrt { x ^ { 2 } + y ^ { 2 } }$

Question

Solve the problem.
-Find a formula for the distance from the point P(x, y, z) to the z-axis. 
A) $\sqrt { z + y }$
B) $\sqrt { x + y }$
C) $\sqrt { \mathrm { z } ^ { 2 } + \mathrm { y } ^ { 2 } }$
D) $\sqrt { x ^ { 2 } + y ^ { 2 } }$

Quizplus · Accepted Answer

The distance from a point P(x, y, z) to the z-axis will be equal to the distance between the point P(x, y, z) and the point on the z-axis directly below it. This point will have coordinates (0,0,z).

Using the distance formula, the distance between P and (0,0,z) is:

\begin{aligned} \sqrt{(x-0)^2 + (y-0)^2 + (z-z)^2} &= \sqrt{x^2 + y^2} \end{aligned}

Therefore, the formula for the distance from point P to the z-axis is $\sqrt { x ^ { 2 } + y ^ { 2 } }$, which is choice D.

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