MP Board Class 11 Mathematics — What are the coordinates o

Q: What are the coordinates of the centroid of a triangle whose vertices are $(x1, y1, z1)$, $(x2, y2, z2)$, and $(x3, y3, z3)?$

The centroid of a triangle with vertices $(x1, y1, z1)$, $(x2, y2, z2)$, and $(x3, y3, z3)$ is given by $\left(\frac{x1+x2+x3}{3}, \frac{y1+y2+y3}{3}, \frac{z1+z2+z3}{3}\right)$.

MP Board · Class 11 · Mathematics · Introduction to Three Dimensional GeometryWhat are the coordinates of the centroid of a triangle whose vertices are $(x1, y1, z1)$, $(x2, y2, z2)$, and $(x3, y3, z3)?$

Step-by-Step Solution

The centroid of a triangle with vertices $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, and $(x_3, y_3, z_3)$ is given by $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}\right)$.

Detailed Options Breakdown

Option : $\left(\frac{x_1+x_2+x_3}{2}, \frac{y_1+y_2+y_3}{2}, \frac{z_1+z_2+z_3}{2}\right)$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Three Dimensional Geometry.

Option 1: $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}\right)$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 2: $(x_1+x_2+x_3, y_1+y_2+y_3, z_1+z_2+z_3)$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Three Dimensional Geometry.

Option 3: $\left(\frac{x_1x_2x_3}{3}, \frac{y_1y_2y_3}{3}, \frac{z_1z_2z_3}{3}\right)$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Three Dimensional Geometry.

💡 Study Guide: This question tests core syllabus concepts from Introduction to Three Dimensional Geometry. For formulas, key summaries, and mock exam reference guides, read the full Introduction to Three Dimensional Geometry Revision Notes.

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Verified by Academic Committee