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Shortest Distance from a Point to a Line

Maths: KS3, topic 4.2.4

Shortest Distance from a Point to a Line

The shortest distance from a point to a straight line is always the perpendicular distance. Here's how to identify it:

Perpendicular Distance

Perpendicular Distance

  • The shortest distance from a point to a line is always the perpendicular line.
  • This means the line connecting the point to the original line must form exactly a 90∘90^\circangle.
Example 1

Example 1

  • Which path from point P to the line is the shortest?

  • Identify the perpendicular path (the one forming a 90° angle).

  • Compare the measurements. The perpendicular path is 4 cm, while the slanted path is 5 cm.

  • The perpendicular path is always the shortest distance.

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