Q.Find the coordinates of the point dividing the line segment joining $(2, -1)$ and $(8, 5)$ internally in the ratio $2:1$.

Apply the section formula for internal division with $m:n=2:1$.

With $A(x_1,y_1)=(2,-1)$, $B(x_2,y_2)=(8,5)$, and ratio $m:n=2:1$, the section formula gives

$y=\dfrac{(2)(5)+(1)(-1)}{2+1}=\dfrac{10-1}{3}=\dfrac{9}{3}=3$ …

As with every section-formula problem, mixing up which endpoint's coordinates carry the weight $m$ versus $n$ is the most frequent error; here $B$' …