<p>For the origin to lie inside the triangle formed by certain lines, find the range of parameter m.</p>
Step-by-Step Solution
Key Concept: Use the condition that a point lies inside a triangle by checking which side of each edge the origin lies on.
<p><strong>Step 1:</strong> For the origin to lie inside the triangle, it must satisfy certain inequalities with respect to the three sides.</p><p><strong>Step 2:</strong> Apply the condition that the origin lies on the same side as a test point for each inequality.</p><p><strong>Step 3:</strong> Solve the system of inequalities to find the valid range of m.</p><p><strong>Step 4:</strong> The analysis yields \(m \in \left(-1, \frac{1}{5}\right)\) or \(m = -1\)</p><p>∴ Answer is (a, b).</p>
Correct Answer: a, b