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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Step 1: $x = \frac{3 + k}{2}$ and $y = \frac{4 + 6}{2} = 5$
Step 2: $	herefore \frac{3 + k}{2} + 5 - 10 = 0$
Step 3: $\frac{3 + k}{2} = 5 \Rightarrow 3 + k = 10 \Rightarrow k = 7$

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