If (a, b) is the midpoint of the line segment connecting the points (-7, 14) and (k, 4) and the equation of line is 2a + 3b = 5 then find out k.

The midpoint of two points $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ and $\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)$ is calculated by the formula: $\left(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}\right)$

So, let the midpoint of $(-7,14) \&\hspace{0.17em}(\mathrm{k}, 4) \mathrm{be} (\mathrm{a}, \mathrm{b})$

On substitution, we get:

$\Rightarrow \left(\frac{-7+\mathrm{k}}{2},\frac{14+4}{2}\right)=(\mathrm{a},\mathrm{b})$

$\Rightarrow \mathrm{a}=\frac{-7+\mathrm{k}}{2}; \mathrm{b}=9$

Given equation of the line: 2a + 3b = 5

On substitution, we get:

 $\Rightarrow 2\times \frac{(-7+\mathrm{k})}{2}+3\left(9\right)=5$

$\Rightarrow -7 + k +27=5$

$\Rightarrow k + 20=5$

$\Rightarrow k =5 - 20$

$\Rightarrow k =-15$