Straight Lines
Collinearity of Three Points
Grade 11
Question:
<p>Find the value of <p>m</p> such that the points <p>(1, 2)</p>, <p>(2, -1)</p>, and <p>(−1, 3)</p> are collinear.</p>
Step-by-Step Solution
Key Concept: Three points are collinear if and only if the determinant formed by their coordinates equals zero.
<p><strong>Step 1:</strong> For three points to be collinear, the determinant must equal zero:</p><p>$$\begin{vmatrix} 1 & 2 & -1 \\ 2 & -1 & m \\ -1 & 3 & 1 \end{vmatrix} = 0$$</p><p><strong>Step 2:</strong> Expanding the determinant:</p><p>$$5m + 5 = 0$$</p><p><strong>Step 3:</strong> Solving for <p>m</p>:</p><p>$$m = -1$$</p><p>∴ Answer is <strong>−1</strong>.</p>
Correct Answer: -1