Final answer:
The student is asked to find the variable and the length of AC given that B is the midpoint. After computation, none of the provided options fulfill the criteria that AC should be exactly twice the length of x, therefore indicating a possible error in the question or answer choices.
Step-by-step explanation:
The question asks us to determine the variable and the length of segment AC when point B is the midpoint. If B is the midpoint of AC, the length from A to B, which we call AB, should be equal to the length from B to C, which we designate as BC. Since B is the midpoint, AB (or BC) would be half of AC. Given the values for x and AC in the options, we can assess if AB or BC is half of AC to find the correct answer.
For example, in option a), if x is the length AB (or BC) and is given as 8, then doubling it should give us AC. If AC = 18, then 2x (2*8) does not equal 18, so this is not the correct solution. We can use this method to evaluate the other options:
- b) x = 4, AC should be 2x = 8, but AC is given as 20, so this is incorrect.
- c) x = 6, AC should be 2x = 12, but AC is given as 16, so this is incorrect.
- d) x = 5, AC should be 2x = 10, but AC is given as 17. Although none of the options provided perfectly match the criteria that AC should be twice the length of x, option d) comes closest without going over the value of AC.
However, all the given options contain inconsistencies as no option exactly fulfills the condition that 2x should equal AC if B is supposed to be the exact midpoint of AC.