Bilal M.

asked • 02/22/16

find the distance from the point to the x-axis

find the distance from the point (-5,2,-3) to the x-axis

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Kenneth S. answered • 02/22/16

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I attempted a 3D sketch.  From this I visualized a right triangle in the plane that is parallel to the z axis and perpendicular to the x axis and passes through (-5, 2, -3).  This right triangle has legs measuring 2 and 3 units.
 
I think I see a path down to the x-axis by traveling down the leg of length 2 and then (right turn) across the leg of length 3 to arrive at the x-axis.  But that's not the shortest way to get there; travel down the hypotenuse would be a distance of square root of (22 + 32), so what I get is √13.
 
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Elwyn D.

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Absolutely, the distance is the shortest distance from that point to any point on the line.  That shortest distance will be from the point (-5,0,0) to the x-axis, so the y and z coordinates of any point on the x-axis will be 0 and 0, respectively.  Any value, a, other than -5 for the x value will add another value (-5 -a)2 to the argument of the distance equation.  Since the value is squared, it will increase the argument of the square root function.  Increasing the argument will necessarily increase the distance, therefore your other proposed distance would be greater than the distance to (-5,0,0), therefore it would not be the correct distance from (-5,-2,3) to the x-axis.  
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02/22/16

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