Question

in the figure below, b lies between a and c. find the location of b so that ( ab ) is ( \frac{1}{3} ) of ( ac ). the number line shows a at -16, c at 5, and b at ?. there is a text box labeled location of b : with a placeholder, and two buttons: one with 5 and one with ×.

Explanation:

Step1: Calculate the length of AC

The coordinate of A is -16 and the coordinate of C is 5. The length of \( AC \) is \( |5 - (-16)| = |5 + 16| = 21 \).

Step2: Find the length of AB

Since \( AB=\frac{1}{3}AC \), substitute \( AC = 21 \) into the formula, we get \( AB=\frac{1}{3}\times21 = 7 \).

Step3: Calculate the coordinate of B

To find the coordinate of B, we start from A and move 7 units towards C. The coordinate of A is -16, so the coordinate of B is \( -16 + 7=-9 \).

Answer:

-9