Question

HELP
Suppose A has a coordinate of 8 and AB = 3. What are the possible midpoints of AB?

Answer 1

The possible midpoints of AB are
`(19)/(2)` and
`(13)/(2)`.

Explanation:

Let suppose that A and B have one-dimensional coordinates. GIven that
`A = 8` and
`AB = 3`, there are two possible locations for B:

`B_(1) = A+AB`

`B_(1) =8+3`

`B_(1) = 11`

`B_(2) = A-AB`

`B_(2) = 8-3`

`B_(2) = 5`

The midpoint equations for each case are, respectively:

`m_(1) = (A+B_(1))/(2)`

`m_(1)=(8+11)/(2)`

`m_(1) = (19)/(2)`

`m_(2) = (A+B_(2))/(2)`

`m_(2) = (5+8)/(2)`

`m_(2) = (13)/(2)`

The possible midpoints of AB are
`(19)/(2)` and
`(13)/(2)`.