Determine the midpoint of the line segment connecting (3,0) and (-1,4).

We know, Midpoint $\mathrm{M}(\mathrm{x},\mathrm{y})$ of the line segment joining the points $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ and $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ is:

$\mathrm{M}(\mathrm{x},\mathrm{y})=\left(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}\right)$

Thus, The midpoint of the line segment joining the points (3,0) and (-1,4) is:

$\mathrm{M}(\mathrm{x},\mathrm{y})=\left(\frac{3-1}{2},\frac{0+4}{2}\right)$

$\mathrm{M}(\mathrm{x},\mathrm{y})=\left(\frac{2}{2},\frac{4}{2}\right)$

$\mathrm{M}(\mathrm{x},\mathrm{y})=\left(1,2\right)$

Hence, M(x, y) = (1, 2)