Shortest Path Intuition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
What is the shortest distance from point P(4,3)P(4, 3) to the origin? Justify that the straight line gives the minimum.

Solution

  1. 1
    Step 1: Distance =42+32=25=5= \sqrt{4^2 + 3^2} = \sqrt{25} = 5 units.
  2. 2
    Step 2: Any other path from PP to the origin would zigzag or curve, and by the triangle inequality would be longer than 55.

Answer

Shortest distance =5= 5 units (straight line).
The direct (straight-line) distance is always the minimum in Euclidean space. The distance formula computes this minimum path length. Any detour adds length.

About Shortest Path Intuition

The minimum-length route connecting two points, whose form depends on the geometry of the underlying space.

Learn more about Shortest Path Intuition →

More Shortest Path Intuition Examples

Example 1 medium

A river runs along the [formula]-axis. Town [formula] is at [formula] and town [formula] is at [form

Example 2 hard

What is the shortest path between two points in the Euclidean plane, and why? Then explain why the s

Example 4 hard

An ant on the surface of a unit cube wants to travel from vertex [formula] to the opposite vertex [f

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Related Concepts

Distance