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Find the length of the segment from the point (1, 2) to the line x + y + 5 = 0, if the measurement is taken along a line parallel to 3x − y = 7.

1. 4√10
2. 40
3. √40
4. 10√2

Correct answer: √40

Solution

Move from (1,2) along direction (1,3): (1+t, 2+3t). Hitting x+y+5=0 gives 3+4t+5=0, t = -2. Distance = |t|*sqrt(1+9) = 2*sqrt(10) = sqrt(40).

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