A structural engineer is fixing a diagonal support strut from a fixed point \(P\) on a workshop ceiling down to the horizontal beam \(AB\) shown in the diag...
Question 1 Report
A structural engineer is fixing a diagonal support strut from a fixed point \(P\) on a workshop ceiling down to the horizontal beam \(AB\) shown in the diagram, so that the strut meets the beam at right angles for maximum strength.
Using a ruler and compasses only, construct the perpendicular from point \(P\) to the line \(AB\). Show all your construction arcs. (2)
Answer Details
A structural engineer needs a diagonal support strut from a fixed ceiling point \(P\) down to the horizontal beam \(AB\), meeting it at right angles for maximum strength. Dropping the perpendicular from P to line \(AB\) finds the single point on \(AB\) that is closest to P, since the shortest distance from a point to a line is always measured along the perpendicular to that line.
- With the compass point on P, draw an arc with a radius large enough to cross line \(AB\) at two points. Both crossing points are the same distance from P. [1]
- Using the same or a different fixed radius, draw two more arcs centred on those crossing points, on the opposite side of \(AB\) from P, so that they intersect each other. Since this new intersection point and P are both equidistant from the same two points on \(AB\), the straight line through P and this intersection point is the perpendicular to \(AB\). [1]
The two arcs from the line must be struck from the far side, away from the starting point, otherwise they cannot cross and locate the foot of the perpendicular.
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