If P (2, 6) is the mid-point of the line segment joining

It is given that mid-point of line segment joining A (6, 5) and B (4, y) is P (2, 6)

In general to find the mid-point $\mathrm{P}(x, y)$ of two points $\mathrm{A}\left(x_{1}, y_{1}\right)$ and $\mathrm{B}\left(x_{2}, y_{2}\right)$ we use section formula as,

$\mathrm{P}(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

So,

$(2,6)=\left(\frac{4+6}{2}, \frac{y+5}{2}\right)$

Now equate the y component to get,

$\frac{y+5}{2}=6$

So,

$y=7$