Unit 1ProjectionsHARD
Shortest Distance from Point to Line
A line PQ has P at (20, 30, 15) and Q at (60, 10, 45). Find the shortest distance from a point R at (40, 40, 25) to the line PQ. All dimensions in mm.
7,600 views
Solution Diagram
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Step-by-Step Construction
- 1
Draw projections of line PQ using the given coordinates
- 2
Plot point R in both views
- 3
Draw perpendicular from R to line PQ in both views
- 4
The shortest distance appears in the view where line shows true length
- 5
Use auxiliary projection to find true length of line PQ
- 6
In this view, draw perpendicular from R and measure the distance
- 7
Verify using analytical method: distance = ||(R-P) × (Q-P)|| / ||Q-P||
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