If A and B are the points respectively $\displaystyle ( -6,\ 7)$ and $\displaystyle ( -1,\ -5)$ respectively, Then the distance 2AB is equal to:
$( A) \ 13$
$( B) \ 26$
$( C) \ 169$
$( D) \ 238$
Given: Here given two points $A( -6,\ 7)$ and $B( -1,\ -5)$.
To do: To find out the distance $2AB=?$
Solution:
we know if there two points $( x_{1} ,\ y_{1})$ and $( x_{2} ,\ y_{2})$,
distance between the two points,$=\sqrt{( x_{2} -x_{1})^{2} +( y_{2} -y_{1})^{2}}$
By putting the values of $A( -6,\ 7)$ and $B( -1,\ -5)$ in the above formula
$AB=\sqrt{\left(( -6+1)^{2} +( 7+5)^{2} \ \right)}$
$\Rightarrow AB=\sqrt{\left(( -5)^{2} +( 12)^{2} \ \right)}$
$\Rightarrow AB=\sqrt{( 25+144)}$
$\Rightarrow AB=\sqrt{169}$
$\Rightarrow AB=13$
$\therefore 2AB=2\times 13=26$
$\therefore$ Option $( B)$ is correct.
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