If$P\left(\frac{a}{2} ,4\right)$ is the mid-point of the line segment joining the points $A( -6,\ 5)$ and $( -2,\ 3)$, then the value of a is:
$( A) \ -8$
$( B) \ \ 3$
$( C) \ -4$
$( D) \ \ 44$
Given: A line segment joining the points $A( -6,\ 5)$ and$B( -2,\ 3)$ and its mid-point $P\left(\frac{a}{2} ,\ 4\right)$
To do: To find out the value of $a=?$
Solution: If there is a line segment joining two points$ ( x_{1} ,\ y_{1} )$ and $( x_{2} ,\ y_{2})$,
Then its mid-point $( x,\ y) =\left(\frac{x_{1} +x_{2}}{2} ,\ \frac{y_{1} +y_{2}}{2}\right)$
Similarly $P\left(\frac{a}{2} ,4\right) =\left(\frac{-6-2}{2} ,\frac{5+3}{2}\right)$
$\Rightarrow \ P\left(\frac{a}{2} ,4\right) =\left(\frac{-8}{2} ,\frac{8}{2}\right)$
$\Rightarrow \ P\left(\frac{a}{2} ,4\right) =\left(\frac{-8}{2} ,4\right)$
$\Rightarrow \frac{a}{2} =\frac{-8}{2}$
$\Rightarrow a=-4$
$\therefore$ Option $( A)$ is correct.
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