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MP Board · Class 10 · Mathematics · Coordinate GeometryThe point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3:1$ internally is:

Q: The point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3:1$ internally is:

Using the section formula $\left(\frac{m1x2 + m2x1}{m1 + m2}, \frac{m1y2 + m2y1}{m1 + m2}\right)$, with $m1=3, m2=1, x1=4, y1=-3, x2=8, y2=5$, we get $\left(\frac{3(8) + 1(4)}{3 + 1}, \frac{3(5) + 1(-3)}{3 + 1}\right) = \left(\frac{24 + 4}{4}, \frac{15 - 3}{4}\right) = \left(\frac{28}{4}, \frac{12}{4}\right) = (7, 3)$. Therefore, the correct option is B.

Step-by-Step Solution

Using the section formula $\left(\frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2}\right)$, with $m_1=3, m_2=1, x_1=4, y_1=-3, x_2=8, y_2=5$, we get $\left(\frac{3(8) + 1(4)}{3 + 1}, \frac{3(5) + 1(-3)}{3 + 1}\right) = \left(\frac{24 + 4}{4}, \frac{15 - 3}{4}\right) = \left(\frac{28}{4}, \frac{12}{4}\right) = (7, 3)$. Therefore, the correct option is B.

Detailed Options Breakdown

Option : (3, 7)

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.

Option 1: (7, 3) (Correct Answer)

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

Option 2: (5, 2)

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.

Option 3: (2, 5)

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.

💡 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.

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