Find the coordinates of the point that divides the line segment joining $A (- 2, 5)$ and $B (6, - 3)$ in the ratio $4 : 1$ internally.

medium 2 marks Class 10 · Mathematics · Coordinate Geometry

Answer

(\frac{22}{5}, - \frac{7}{5})

The correct answer is $(\frac{22}{5}, - \frac{7}{5})$ — Hence the required point is $(\frac{22}{5}, - \frac{7}{5})$ .

Step-by-step solution

Recall the section formula for internal division: if a point $P$ divides $A B$ in the ratio $m : n$ , then $P (\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})$ .
Here $m = 4$ , $n = 1$ , $A (x_{1}, y_{1}) = (- 2, 5)$ and $B (x_{2}, y_{2}) = (6, - 3)$ .
Compute the x‑coordinate: $x = \frac{4 \cdot 6 + 1 \cdot ( - 2 )}{4 + 1} = \frac{24 - 2}{5} = \frac{22}{5}$ .
Compute the y‑coordinate: $y = \frac{4 \cdot ( - 3 ) + 1 \cdot 5}{5} = \frac{- 12 + 5}{5} = \frac{- 7}{5}$ .
Hence the required point is $(\frac{22}{5}, - \frac{7}{5})$ .

Common mistake: Interchanging the coordinates of

A

and

B

or using the ratio

n : m

instead of

m : n

Concept tested: Section formula (internal division)

Published 23 August 2026 · Last updated 24 August 2026 · How this solution was prepared and checked