COMEDK · Maths · 10. Straight Lines
The point on the line \(x+y=4\) that lie at a unit distance from the line \(4 x+3 y=10\) is
- A \((-7,11)\)
- B \((5,-1)\)
- C \((2,2)\)
- D \((3,-1)\)
Answer & Solution
Correct Answer
(A) \((-7,11)\)
Step-by-step Solution
Detailed explanation
Let the point on the line \(x+y=4\) be \(P(h, 4-h)\). The distance \(d\) of point \(P(h, 4-h)\) from the line \(4x+3y-10=0\) is given by the formula \(d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}\). Substituting the coordinates of \(P\) and the line equation:…
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