Find the coordinates of the point which divides the join of A

Solution:

Let P(x, y) be the point that divides the join of A(-5, 11) and B(4, -7) in the ratio 2 : 7

Formula: If $m_{1}: m_{2}$ is the ratio in which the join of two points is divided by another point $(x, y)$, then

$\mathrm{x}=\frac{\mathrm{m}_{1} \mathrm{x}_{2}+\mathrm{m}_{2} \mathrm{x}_{1}}{\mathrm{~m}_{1}+\mathrm{m}_{2}}$

$\mathrm{y}=\frac{\mathrm{m}_{1} \mathrm{y}_{2}+\mathrm{m}_{2} \mathrm{y}_{1}}{\mathrm{~m}_{1}+\mathrm{m}_{2}}$

Here, $x_{1}=-5, x_{2}=4, y_{1}=11$ and $y_{2}=-7$

Substituting,

$x=\frac{2 \times 4+7 \times-5}{2+7}$

$x=\frac{8-35}{9}$

$x=\frac{-27}{9}$

$\Rightarrow x=-3$

$y=\frac{2 \times-7+7 \times 11}{2+7}$

$y=\frac{-14+77}{9}$

$y=\frac{63}{9}$

$\Rightarrow y=8$

 Therefore, the coordinates of the point which divided the join of A(-5, 11) and B(4, -7) in the ratio 2 : 7 is (-3, 8).