NCERT · Class 10 · Mathematics · Coordinate GeometryThe centroid of a triangle whose vertices are $(x1, y1)$, $(x2, y2)$ and $(x3, y3)$ is given by:
Step-by-Step Solution
The formula for the centroid of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is $\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)$. Therefore, the correct option is D.
Detailed Options Breakdown
Option : (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.
Option 1: (x_1 + x_2 + x_3, y_1 + y_2 + y_3)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.
Option 2: (\frac{x_1 - x_2 - x_3}{3}, \frac{y_1 - y_2 - y_3}{3})
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.
Option 3: (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
💡 Study Guide: This question tests core syllabus concepts from Coordinate Geometry. For formulas, key summaries, and mock exam reference guides, read the full Coordinate Geometry Revision Notes.