Question

B is the midpoint of AC. What is the length of AB? AB is 9x+7 and BC is -3x+20

Answer 1

`AB = (67)/(4)\\`

Explanation:

If
`B` is the midpoint of
`\overline{AC}` then
`AB` is just half of
`AC` and also,
`BC` is just half of
`AC`. This means that
`AB` must be equal to
`BC`. Essentially,
`9x +7 = -3x +20` and we can solve for the of
`x` from that equation.

`9x +7 = -3x +20 \\ 9x +7 +3x = -3x +20 +3x \\ 12x +7 = 20 \\ 12x +7 -7 = 20 -7 \\ 12x = 13 \\ (12x)/(12) = (13)/(12) \\ x = (13)/(12)`

Now we can solve for
`AB`

`AB = 9((13)/(12)) +7 \\ AB = 3((13)/(4)) +7 \\ AB = (39)/(4) +7 \\ AB = (39)/(4) +(28)/(4) \\ AB = (67)/(4)`