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If the mid-point of the line segment joining the points A$(3, 4)$ and B$(k, 6)$ is P$(x, y)$ and $x + y - 10 = 0$, then find the value of $k$.
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$x = \frac{3+k}{2}$
and $y = \frac{4+6}{2} = 5$
$\frac{3+k}{2} + 5 - 10 = 0$
$\Rightarrow k = 7$
and $y = \frac{4+6}{2} = 5$
$\frac{3+k}{2} + 5 - 10 = 0$
$\Rightarrow k = 7$