Straight Lines
Triangle formed by lines
Grade 11
Question:
<p>Two sides of a triangle have the joint equation \((x - 3y + 2)(x + y - 2) = 0\), the third side which is variable always passes through the point \((-5, -1)\), then possible values of slope of third side such that origin is an interior point of triangle is/are:</p>
<p>(a) \(-\frac{4}{3}\)</p>
<p>(b) \(-\frac{2}{3}\)</p>
<p>(c) \(-\frac{1}{3}\)</p>
<p>(d) \(\frac{1}{6}\)</p>
Step-by-Step Solution
Key Concept: The origin must satisfy inequalities representing the interior of the triangle formed by all three lines.
<p>The two sides have equations \(x - 3y + 2 = 0\) and \(x + y - 2 = 0\). The third side passes through \((-5, -1)\) and has a variable slope. For the origin to be an interior point of the triangle, the third side must have a slope such that the origin lies strictly inside the triangle formed by the three lines.</p>
Correct Answer: a, b, c, d