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(a, $2 \mathrm{~b}$ ) is the mid-point of the line segment joining the points $(10,-6)$ and $(\mathrm{k}, 4)$. If $\mathrm{a}-2 \mathrm{~b}=7$, then what is the value of $\mathrm{k}$ ?
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$M \equiv$ mid point of line segment $P Q$
$\frac{K+10}{2}=a \Rightarrow K=(2 a-10)$
$2 b=\frac{4-6}{2}=-1$
given $a-2 b=7$...(1)
Put the values of $a$ \& $b$ in $e q(1)$, we get
$\frac{K+10}{2}+1=7$
$\frac{K+10}{2}=6 \Rightarrow K=12-10$
$K=2$
$\frac{K+10}{2}=a \Rightarrow K=(2 a-10)$
$2 b=\frac{4-6}{2}=-1$
given $a-2 b=7$...(1)
Put the values of $a$ \& $b$ in $e q(1)$, we get
$\frac{K+10}{2}+1=7$
$\frac{K+10}{2}=6 \Rightarrow K=12-10$
$K=2$
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