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The midpoint of line AB is M(6,1).if the coordinates of A are (4,8), what are the coordinates of B?

User Dupree
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\Large\underline{\rm Solution :- }

Midpoint formula :
\bigg((x_1+x_2)/(2),(y_1+y_2)/(2)\bigg)

Here the midpoint of A and B is
(6,1) and the given point is
A(4,8) . We need to find the coordinates of B . So , let the point be
(x_2,y_2)


\implies (6,1) =\bigg((4+x_2)/(2),(8+y_2)/(2)\bigg)

Compare ,


\implies 6 = (4+x_2)/(2)\\\\\implies 12 = 4 + x_2 \\\\\implies \boxed{ x_2 = 8 }

And ,


\implies 1 = (y_2+8)/(2)\\\\\implies 2 = 8 + y_2 \\\\\implies y_2 = 2-8 \\\\\implies\boxed{ y_2 = -6}

Hence the required coordinate is
( 8,-6) .

User Crrlos
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