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:
 $am = \frac{ab}{2}$
 Therefore, substituting values we have:
 $2x+9 = \frac{8x-50}{2}$
 From here, we clear the value of x.
 We have then:
 $2x+9 = 4x-25$
 $9+25 = 4x-2x$
 $34 = 2x$
 $x = \frac{34}{2}$
 $x = 17$
 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:
 $am=43$