<p>The orthocentre of a triangle is at origin and circumcentre is at (2, –3). Then the centroid of the triangle is:</p>
Step-by-Step Solution
Key Concept: The Euler line relationship states that centroid G divides the line segment from orthocenter H to circumcenter C in the ratio 1:2, i.e., HG:GC = 1:2, giving G = H + (1/3)(C - H).
<p><strong>Step 1:</strong> Recall the Euler line property: The orthocenter (H), centroid (G), and circumcenter (C) are collinear, and G divides HC in the ratio HG:GC = 1:2.</p><p><strong>Step 2:</strong> Using the section formula, if G divides HC in ratio 1:2 internally:</p><p>G = H + (1/3)(C - H) = (1/3)C + (2/3)H</p><p><strong>Step 3:</strong> Substitute H = (0, 0) and C = (2, -3):</p><p>G = (1/3)(2, -3) + (2/3)(0, 0)</p><p>G = (2/3, -1)</p><p>∴ Answer: B</p>
Correct Answer: B