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📐 Mathematics  ·  Introduction to Three Dimensional Geometry  ·  JEE

Why does a point's distance from a coordinate axis use only two of its three coordinates?

Answer: The perpendicular from the point meets the axis at the foot sharing that axis coordinate, so that coordinate contributes nothing.

  • A Distances in space are always computed pairwise between two coordinates only
  • B The third coordinate is always zero for points measured from an axis
  • C The perpendicular from the point meets the axis at the foot sharing that axis coordinate, so that coordinate contributes nothing
  • D Every axis lies in the XY-plane, making the third coordinate irrelevant

Correct answer: C. The perpendicular from the point meets the axis at the foot sharing that axis coordinate, so that coordinate contributes nothing

Explanation: The foot of the perpendicular from P to the x-axis is (x, 0, 0), so the difference in the x-coordinate is zero and only y and z survive in the formula.

zxyOP(x, y, z)first octant:x>0, y>0, z>0

Concept context

Coordinate axes and planes in space, octants, distance between two points, and the section formula

Read the full Introduction to Three Dimensional Geometry notes →