Question

Point M is between points A and B on segment AB.

Atte 4D Sec AM = 2x+7, MB = 5x-3, and AB = 32.
a. Write an equation using the Segment Addition Postulate (using the points and not the
expressions) ie CD+DEEEF
b. Use the equation to solve for x.
c. What is the length of AM?
d. What is the length of MB?
e. Is M the midpoint of AB? Yes/No

Answer 1

By applying the Segment Addition Postulate, we find that x equals 4. The lengths of segments AM and MB are 15 and 17, respectively. Point M is not the midpoint of AB as AM does not equal MB.

Step-by-step explanation:

To solve for x, we use the Segment Addition Postulate which states that if point M is between points A and B on segment AB, then AM + MB = AB. The equation following this postulate would be:

AM + MB = AB

We are given AM = 2x + 7, MB = 5x - 3, and AB = 32. By substituting these expressions into the equation we get:

2x + 7 + 5x - 3 = 32

To find the value of x, we combine the like terms:

7x + 4 = 32

Subtract 4 from both sides:

7x = 28

Divide both sides by 7 to get:

x = 4

Now, to find the lengths of AM and MB, we substitute x back into the expressions:

AM = 2(4) + 7 = 15

MB = 5(4) - 3 = 17

Since AM + MB equals AB and their values are not equal, point M is not the midpoint of segment AB.