The two points on the line $x+y=4$ that lie at a unit distance from the line $4 x+3 y=10$ are

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Professor PC Thomas Classes · Answer

Point $(x, 4-x)$. Distance $= \frac{|4x + 3(4-x) - 10|}{5} = 1 \implies |x + 2| = 5 \implies x = 3, -7$.