E-SL04 · A straight track and a reflection
A straight track passes through \(A(1,7)\) and \(B(9,1)\). Point \(P=(5,9)\) lies away from the track. All coordinates are in metres.
Find an equation for the track.
Find the perpendicular foot H from P to the track, and the shortest distance from P to the segment AB.
Find the reflection P′ of P in the track. Verify the midpoint condition.
Complete-answer checking, worked solutions and indicative written criteria.
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