What will be the coordinates of the midpoint of the line segment joining the points (-5, 10) and(15, 2)?
 

Midpoint is something that lies in the center of the line segment
Thus, it divides the line in the ratio of 1: 1.
Using, the section formula: 

 $\mathrm{x}=\frac{{\mathrm{mx}}_2+{\mathrm{nx}}_1}{\mathrm{m}+\mathrm{n}} \mathrm{and} \mathrm{y}=\frac{{\mathrm{my}}_2+{\mathrm{ny}}_1}{\mathrm{m}+\mathrm{n}}$
The points are $\mathrm{A}(-5,10) \mathrm{and} \mathrm{B}(15,2)$ and the ratio is$1:1$.

Here, m = 1, n = 1, x₁ = -5, y₁ = 10, x₂ = 15 and y₂ = 2.

∴ $\mathrm{x}=\frac{1(-5)+1\left(15\right)}{2}=\frac{-5+15}{2}=\frac{10}{2}=5$
$\mathrm{y} = \frac{1\left(2\right)+1\left(10\right)}{2}=\frac{2+10}{2}=\frac{12}{2}=6$
Hence, the point is (5, 6).