Find the coordinates of the midpoints of the line segment joining:

(i) The given points are A(3, 0) and B(−5, 4).
Let (x, y) be the mid point of AB. Then:

$x=\frac{x_{1}+x_{2}}{2}, y=\frac{y_{1}+y_{2}}{2}$

$\Rightarrow x=\frac{3+(-5)}{2}, y=\frac{0+4}{2}$

$\Rightarrow x=\frac{-2}{2}, y=\frac{4}{2}$

$\Rightarrow x=-1, y=2$

Therefore, (−1, 2) are the coordinates of mid point of AB.

(ii) The given points are P(−11, −8) and Q(8, −2).
Let (x, y) be the mid point of PQ. Then:

$x=\frac{x_{1}+x_{2}}{2}, y=\frac{y_{1}+y_{2}}{2}$

$\Rightarrow x=\frac{-11+8}{2}, y=\frac{-8-2}{2}$

$\Rightarrow x=-\frac{3}{2}, y=-\frac{10}{2}$

$\Rightarrow x=-\frac{3}{2}, y=-5$

Therefore, $\left(-\frac{3}{2},-5\right)$ are the coordinates of midpoint of $P Q$.