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Find the coordinates of the point that lies at a distance of +3 from the point (1, -3) on the line 2x + 3y + 7 = 0.

1. (1 - 9/√13, -3 + 6/√13)
2. (1 + 9/√13, 1 - 9/√13)
3. (3 - 6/√13, 3 + 6/√13)
4. (1 + 9/√13, -3 - 6/√13)

Correct answer: (1 + 9/√13, -3 - 6/√13)

Solution

The line 2x+3y+7=0 has direction (3,-2)/sqrt(13). From (1,-3), the point at +3 along it is (1 + 9/sqrt(13), -3 - 6/sqrt(13)). The option with y-coordinate 1 - 9/sqrt(13) is impossible.

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