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Which points on the line x + y = 4 are exactly one unit away from the line 4x + 3y = 10?

1. (3, 1), (−7, 11)
2. (3, 1), (7, 11)
3. (−3, 1), (−7, 11)
4. (1, 3), (−7, 11)

Correct answer: (3, 1), (−7, 11)

Solution

The points (3, 1) and (−7, 11) are both located on the line x + y = 4 and are exactly one unit away from the line 4x + 3y = 10, as verified by calculating the perpendicular distance from these points to the line, which equals one unit.

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