Question

Point M is the midpoint of segment AB. If AM = 50 – 3x and MB = –20 + 4x, find the value of AM AM = -10 AM = 10 AM = -20 AM = 20

Answer 1

If M is the midpoint of segment AB then |AM| = |MB|
|AM| = 50 - 3x|BM| = -20 + 4x

We have the equation:

50 - 3x = -20 + 4x |-50
-3x = -70 + 4x |-4x
-7x = -70 |:(-7)
x = 10
|AM| = 50 - 3x
substitute the value of x:
|AM| = 50 - 3 · 10 = 50 - 30 = 20
Answer: AM = 20