<p>The distance of the point (1, 2) from the line \(x + y + 5 = 0\) measured along the line parallel to \(3x - y = 7\) is equal to:</p>
Step-by-Step Solution
Key Concept: The distance is measured along a line parallel to 3x - y = 7 passing through (1,2). Find where this line intersects x + y + 5 = 0, then calculate the distance between these two points.
<p><strong>Step 1:</strong> Write the equation of line parallel to 3x - y = 7 passing through (1, 2).</p><p>Slope of 3x - y = 7 is 3. Line through (1,2): y - 2 = 3(x - 1) ⟹ 3x - y - 1 = 0</p><p><strong>Step 2:</strong> Find intersection of 3x - y - 1 = 0 and x + y + 5 = 0.</p><p>Adding equations: 4x + 4 = 0 ⟹ x = -1</p><p>From x + y + 5 = 0: -1 + y + 5 = 0 ⟹ y = -4</p><p>Intersection point is (-1, -4)</p><p><strong>Step 3:</strong> Calculate distance between (1, 2) and (-1, -4).</p><p>d = √[(1-(-1))² + (2-(-4))²] = √[4 + 36] = √40 = 2√10</p><p>∴ Answer: <strong>2√10</strong></p>
Correct Answer: A