Question

The midpoint of AB is M(-4,-3). If the coordinates of A are (-1, -2), what

are the coordinates of B?

Answer 1

`B(-7,-4)`

Explanation:

Let the co-ordinates of B be
`(x_(2),y_(2))`

If a point
`M(x,y)` is a mid-point of line segment AB with
`A(x_(1),y_(1))` and
`B(x_(2),y_(2))`, then:

`x=(x_(1)+x_(2))/(2)\\y=(y_(1)+y_(2))/(2)`

Here,
`M(x,y)` is
`M(-4,-3), A(x_(1),y_(1))` is
`A(-1,-2)`.

So,
`x = -4, y = -3, x_(1) = -1, y_(1)=-2`

Plug in the formula and solve for unknowns.

`x=(x_(1)+x_(2))/(2)\\-4=(-1+x_(2))/(2)\\x_(2)=-8+1=-7\\\\y=(y_(1)+y_(2))/(2)\\-3=(-2+y_(2))/(2)\\y_(2)=-6+2=-4`

Therefore, the co-ordinates of point B are
`B(-7,-4)`