Find the coordinates of the point that divides the line segment joining $P (2, 3)$ and $Q (8, - 1)$ in the ratio $3 : 2$ internally.

easy 2 marks Class 10 · Mathematics · Coordinate Geometry

Answer

(\frac{28}{5}, \frac{3}{5})

The correct answer is $(\frac{28}{5}, \frac{3}{5})$ — Thus the required point is $(\frac{28}{5}, \frac{3}{5})$ .

Step-by-step solution

Use the internal section formula $(\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})$ with $m = 3$ , $n = 2$ .
Substitute the coordinates: $x$ ‑coordinate $= \frac{3 \cdot 8 + 2 \cdot 2}{3 + 2} = \frac{24 + 4}{5} = \frac{28}{5}$ .
$y$ ‑coordinate $= \frac{3 \cdot ( - 1 ) + 2 \cdot 3}{3 + 2} = \frac{- 3 + 6}{5} = \frac{3}{5}$ .
Thus the required point is $(\frac{28}{5}, \frac{3}{5})$ .

Common mistake: Swapping the numbers of the ratio or using the external section formula by mistake.

Concept tested: Section formula (internal)