90
If the mid-point of the line segment joining the points $A(3, 4)$ and $B(k, 6)$ is $P(x, y)$ and $x + y - 10 = 0$, find the value of $k$.
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Sol. $P(x, y)$ is the mid – point
$\therefore (x,y) = (\frac{3+k}{2}, \frac{4+6}{2})$
$x = \frac{3+k}{2}, y = 5$
$x+y-10 = 0$
$\frac{3+k}{2} + 5 - 10 = 0$
$k = 7$
$\therefore (x,y) = (\frac{3+k}{2}, \frac{4+6}{2})$
$x = \frac{3+k}{2}, y = 5$
$x+y-10 = 0$
$\frac{3+k}{2} + 5 - 10 = 0$
$k = 7$