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What is the perpendicular distance from the point (-1, 3) to the line 2x + y = 3, measured along the direction of a line whose slope is 1?

1. 2/3
2. √2/3
3. 2√2/3
4. 2√5/3

Correct answer: 2√2/3

Solution

From (-1,3) along (1,1): (-1+t, 3+t). Substituting into 2x+y=3: 2(-1+t)+(3+t)=3 -> 3t = 2, t = 2/3. Distance = |t|*sqrt(2) = 2sqrt(2)/3.

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