A closest point on a finite segment

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Read an original example question

P(t) = (6t, 0, 0), for 0 ≤ t ≤ 1. Q = (1, 1, 0).

Part a

Form an expression for |P(t)−Q|².

Part b

Find the parameter of the closest point on the segment.

Part c

Find the minimum squared distance.

Model solution and review criteria

Part a

D(t) = (6t−1)² + 1.

Use the displacement and sum squares.

Part b

The unconstrained minimum is t = $\frac{1}{6}$ , which lies in [0,1].

Locate the stationary parameter.
Check it against the segment bounds.

Part c

At the interior projection, only the vertical separation remains: 1.

Evaluate at the permitted minimiser.

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