Question

In the following figure, the teacher asks a student named Jerrica to find the length of segment AM. Jerrica sets the two sides equal to each other, does some algebra, and proclaims that the length of segment AM is 8 units long

State whether Jerrica is correct in her conclusion. If she is incorrect, explain the source of her error and give the correct length. In at least four sentences, support your response with a brief explanation. Be sure to include the terms midpoint, segment, and bisector in your explanation.

Answer 1

Answer/Step-by-step explanation:

Let us try to find the lenght of AM step-by-step to see if Jessica is correct or incorrect in her conclusion and possibly find out where she made an error if she's incorrect.

Now briefly, keys state some facts that explains or guides us while solving a problem like this:

1. Point M is the midpoint of segment AB.

2. The midpoint M, is a bisector of segment AB.

3. Segment AB is divided into two congruent or equal parts, AM and MB.

4. Therefore, by implication, segment AM (4x - 18) = segment MB (2x - 2).

5. To find the lenght of AM, we need to generate an equation to enable us solve for the value of x.

6. Equation to use to solve using algebra can be gotten by setting segment AM equal to segment MB. Which gives us:

4x - 18 = 2x - 2

Solve for x. Combine like terms.

4x - 2x = 18 - 2

2x = 16

Divide both sides by 2

x = 8

To find the lenght of AM = 4x - 18, replace x with 8 in the expression for the lenght of segment AM. (Note: this is what Jessica failed to do. She assumed 8 to be the length of segment AM.)

AM = 4(8) - 18 (Substitution)

AM = 32 - 18

Length of segment AM = 14 units

Jessica's error was her assuming that x = 8, is the length of segment AM. Her conclusion is wrong.

She ought to have plug in the value of x into the expression given for the lenght of segment AM.