Question

For a line segment AB, one endpoint is A(0,6) and the midpoint is M(4,7) how do you find the coordinates of endpoint B?

Answer 1

The change in `x` and `y` respectively from A at `(0,6)` to M at `(4,7)` are

`Delta x_(AM) = 4`
and
`Delta y_(AM) = 1`

Since M is the midpoint between A and B
`Delta x_(MB) = Delta x_(AM)`
and
`Delta y_(MB) = Delta y_(AM)`

B is located at `M + (Delta x_(MB),Delta y_(MB))`

`=(4+4,7+1) = (8,8)`