Question

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

Answer 1

`\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)` .