Q.Find the mid-point of the line segment joining the points $(-3, 5)$ and $(7, -1)$.

The mid-point is the special case of the section formula with ratio $1:1$, so it is simply the average of the two points' coordinates. …

The mid-point of the segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is the average of the two points' coordinates,

which is the section formula with $m=n=1$.

Here $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(7,-1)$, so …

A frequent slip is dividing by $2$ only one of the two coordinate sums, or mishandling the negative sign when one coordinate is negative (writing $5+(-1)$ as …