Question

The distance of the line \(2x - 3y = 4\) from the point \((1, 1)\) measured parallel to the line \(x + y = 1\) is

• A. \(\sqrt{2}\)
• B. \(5/\sqrt{2}\)
• C. \(1/\sqrt{2}\)
• D. 6

Hint:

Distance measured parallel to given line means along that direction.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Line parallel to \(x + y = 1\) through \((1, 1)\): \(x + y = 2\).
Step 2: Detailed Explanation:
Find intersection of \(2x - 3y = 4\) and \(x + y = 2\)
Solving: \(x = 2\), \(y = 0\)
Distance from \((1, 1)\) to \((2, 0)\) = \(\sqrt{(2 - 1)^2 + (0 - 1)^2} = \sqrt{2}\)
Step 3: Final Answer:
Distance = \(\sqrt{2}\).