In what ratio does the point, P (−3, 3), divide the line segment joining the points A (−4, −1) and B (−2, 7) internally?

Let P (−3, 3) divide the line segment joining the points A (−4, −1), and B (−2, 7) in the ratio k : 1.

By section formula, we know that the coordinate of the point which divides the line segment joining the points (x₁, y₁) and (x₂, y₂) internally, in the ratio

m: n are $\left(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n}\right)$.

$\left(-3,3\right)=\left(\frac{k\times \left(-2\right)+\left(-4\right)}{k+1},\frac{k\times \left(7\right)+\left(-1\right)}{k+1}\right)=\left(\frac{-2k-4}{k+1},\frac{7k-1}{k+1}\right)$

$\Rightarrow -3=\frac{-2k-4}{k+1},3=\frac{7k-1}{k+1}$

$\Rightarrow -2k-4=-3k-3$

$\Rightarrow k=1$

$\therefore k : 1 = 1:1$

Thus, point P divides the line segment joining the points A and B internally in the ratio 1:1.