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NCERT · Class 11 · Mathematics · Introduction to Three Dimensional GeometryWhat is the midpoint of the line segment joining the points $(2, 3, 4)$ and $(4, 1, -2)?

Q: What is the midpoint of the line segment joining the points $(2, 3, 4)$ and $(4, 1, -2)?

The midpoint formula is $\left(\frac{x1+x2}{2}, \frac{y1+y2}{2}, \frac{z1+z2}{2}\right)$. Substituting the values: $\left(\frac{2+4}{2}, \frac{3+1}{2}, \frac{4+(-2)}{2}\right) = \left(\frac{6}{2}, \frac{4}{2}, \frac{2}{2}\right) = (3, 2, 1)$.

Step-by-Step Solution

The midpoint formula is $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}, \frac{z_1+z_2}{2}\right)$. Substituting the values: $\left(\frac{2+4}{2}, \frac{3+1}{2}, \frac{4+(-2)}{2}\right) = \left(\frac{6}{2}, \frac{4}{2}, \frac{2}{2}\right) = (3, 2, 1)$.

Detailed Options Breakdown

Option : (3, 2, 1) (Correct Answer)

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

Option 1: (1, 1, 3)

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

Option 2: (6, 4, 2)

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

Option 3: (3, 1, 2)

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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