What will be the coordinates of the point which divides the line segment joining the points A(-2, 2) and B(-1, 5) in the ratio 2: 5?
 

Given: The points are A(- 2, 2) & B(- 1, 5) and the ratio is 2 : 5.

By using the, section formula:  $\mathrm{x}=\frac{{\mathrm{mx}}_2+{\mathrm{nx}}_1}{\mathrm{m}+\mathrm{n}} \mathrm{and} \mathrm{y}=\frac{{\mathrm{my}}_2+{\mathrm{ny}}_1}{\mathrm{m}+\mathrm{n}}$

Here, m = 2, n = 5, x₁ = -2, y₁ = 2, x₂ = -1 and y₂ = 5.

On substitution, we get:

∴ $\mathrm{x}=\frac{2(-1)+5(-2)}{2+7} = \frac{-2-10}{9}=\frac{-12}{9}=\frac{-4}{3}$

Also,

$\mathrm{y}=\frac{2\left(5\right)+5\left(2\right)}{2+7}=\frac{10+10}{9}=\frac{20}{9}$
Hence, the point is $(-\frac{4}{3},\frac{20}{9})$.