Question

Point m is the midpoint of ab¯¯¯¯¯ . am=2x+9, and ab=8x−50. what is the length of am¯¯¯¯¯¯ ?

Answer 1

Since m is the midpoint of ab, then the following relationship is fulfilled:

`am = (ab)/(2)`
Therefore, substituting values we have:

`2x+9 = (8x-50)/(2)`
From here, we clear the value of x.
We have then:

`2x+9 = 4x-25`

`9+25 = 4x-2x`

`34 = 2x`

`x = (34)/(2)`

`x = 17`
Then, the value of am, is given by substituting x in the expression:

`am=2x+9`
Substituting we have:

`am=2(17)+9`

`am=34+9`

`am=43`
Answer:
the length of am is:

`am=43`