Question

If (-1, 5) is midpoint of line joining the points(-4,a) ;(2, 8)then the value of a is

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Midpoint of the line joining (-4,a) and (2,8) is (-1,5)}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 'a'}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Midpoint formula:}}$

$\mathsf{Midpoint\;of\;the\;line\;segment\;joining\;(x_1,y_1)\;and\;(x_2,y_2)\;is}$

$\mathsf{\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

$\textsf{Midpoint of the line joining (-4,a) and (2,8) = (-1,5)}$

$\mathsf{\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)=(-1,5)}$

$\mathsf{\left(\dfrac{-4+2}{2},\dfrac{a+8}{2}\right)=(-1,5)}$

$\mathsf{\left(\dfrac{-2}{2},\dfrac{a+8}{2}\right)=(-1,5)}$

$\mathsf{\left(-1,\dfrac{a+8}{2}\right)=(-1,5)}$

$\implies\mathsf{\dfrac{a+8}{2}=5}$

$\implies\mathsf{a+8=10}$

$\implies\mathsf{a=10-8}$

$\implies\boxed{\mathsf{a=2}}$