 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/9/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

The line has equation

2 x - y + 2 = 0

, with normal vector

(2, - 1)

d = \frac{∣2 ( 4 ) - ( - 6 ) + 2∣}{2 ^{2} + ( - 1 ) ^{2}} = \frac{16}{5} .

(4, - 6) - (16/5) (2, - 1) = (- 12/5, - 14/5)

, which lies on the line and realizes this shortest distance.

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