Q.Find the point which divides the line segment joining $A(-4, 1)$ and $B(2, -3)$ internally in the ratio $3:2$.

Apply the section formula for internal division with $m:n=3:2$; the answer need not come out to whole numbers.

With $A(x_1,y_1)=(-4,1)$, $B(x_2,y_2)=(2,-3)$, and ratio $m:n=3:2$, the section formula gives

$y=\dfrac{(3)(-3)+(2)(1)}{3+2}=\dfrac{-9+2}{5}=-\dfrac{7}{5}$ …

When both the ratio and a coordinate are negative, students often make a sign-arithmetic slip, such as computing $3(2)+2(-4)$ as $6+8=14$ instead of co …