Unit 1ProjectionsHARD

Perpendicular Distance from Point to Plane

A triangular plane ABC has vertices at A(10,20,30), B(50,15,25), C(30,45,40). Find perpendicular distance from point P(40,30,35) to this plane.

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Solution Diagram

Solution diagram for Perpendicular Distance from Point to Plane
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Step-by-Step Construction

  1. 1

    Draw projections of triangle ABC

  2. 2

    Plot point P in both views

  3. 3

    Find edge view of plane ABC by auxiliary projection

  4. 4

    In edge view, plane appears as a line

  5. 5

    Draw perpendicular from P to this edge view line

  6. 6

    This perpendicular distance is the true shortest distance

  7. 7

    Measure and verify using formula: d = |ax₀ + by₀ + cz₀ + d| / √(a² + b² + c²)

Pro Tips

  • •Always verify your measurements with a scale before finalizing the drawing
  • •Use construction lines lightly and darken the final solution
  • •Label all important points and reference lines clearly

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