CBSE 2024 · Region 3 · Set 1 · Q19

Assertion (A) : The point which divides the line segment joining the points A$\displaystyle (1,2)$ and B$\displaystyle (-1,1)$ internally in the ratio $\displaystyle 1$ : $\displaystyle 2$ is $\displaystyle \left(\frac{-1}{3}, \frac{5}{3}\right)$ Reason (R) : The coordinates of the point which divides the line segment joining the points $\displaystyle \mathrm{A}\left(x_{1}, \mathrm{y}_{1}\right)$ and $\displaystyle \mathrm{B}\left(x_{2}, \mathrm{y}_{2}\right)$ in the ratio $\displaystyle \mathrm{m}_{1}: \mathrm{m}_{2}$ are \[\left(\frac{\mathrm{m}_{1} x_{2}+\mathrm{m}_{2} x_{1}}{\mathrm{~m}_{1}+\mathrm{m}_{2}}, \frac{\mathrm{~m}_{1} \mathrm{y}_{2}+\mathrm{m}_{2} \mathrm{y}_{1}}{\mathrm{~m}_{1}+\mathrm{m}_{2}}\right) \]