Let's work through the problem step-by-step.
1. Identify the given information:
- Point A is at 6.
- Point C is at 1.875.
- The ratio \( AC:CB = 3:5 \).
2. Determine the length of \( AC \):
- Since point A is at 6 and point C is at 1.875, the distance \( AC \) can be found by subtracting the coordinate of point C from point A:
[tex]\[
AC = 6 - 1.875 = 4.125 \text{ units}
\][/tex]
3. Set up the ratio equation:
- \( AC \) and \( CB \) are in the ratio of \( 3:5 \). Let the length of \( CB \) be \( x \) units.
- Then, \( AC = \frac{3}{5} x \).
4. Solve for \( x \):
- We already found that \( AC \) is 4.125 units. Using the ratio equation, we get:
[tex]\[
4.125 = \frac{3}{5} x
\][/tex]
- To solve for \( x \), multiply both sides by \( \frac{5}{3} \):
[tex]\[
x = 4.125 \times \frac{5}{3} = 6.875 \text{ units}
\][/tex]
- Thus, \( CB = 6.875 \text{ units} \).
5. Find the total length \( AB \):
- \( AB = AC + CB \).
- So,
[tex]\[
AB = 4.125 + 6.875 = 11.0 \text{ units}
\][/tex]
Therefore, the length of \( \overline{AB} \) is \( 11 \) units, and the correct answer is:
C. [tex]\( AB = 11 \)[/tex] units.
