[tex]\Large\underline{\rm Solution :- }[/tex]
Midpoint formula : [tex]\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)[/tex]
Here the midpoint of A and B is [tex] (6,1) [/tex] and the given point is [tex] A(4,8)[/tex] . We need to find the coordinates of B . So , let the point be [tex](x_2,y_2)[/tex]
[tex]\implies (6,1) =\bigg(\dfrac{4+x_2}{2},\dfrac{8+y_2}{2}\bigg) [/tex]
Compare ,
[tex]\implies 6 = \dfrac{4+x_2}{2}\\\\\implies 12 = 4 + x_2 \\\\\implies \boxed{ x_2 = 8 }[/tex]
And ,
[tex]\implies 1 = \dfrac{y_2+8}{2}\\\\\implies 2 = 8 + y_2 \\\\\implies y_2 = 2-8 \\\\\implies\boxed{ y_2 = -6}[/tex]
Hence the required coordinate is [tex] ( 8,-6)[/tex] .
