Question

if c lies between a and b on (overline{ab}), then (ac + cb = ab). choose the correct statement about (overline{ab}).
a---6.5---c---5.2---b

a. (ab = 2(ac))
b. (ab = 11)
c. (ab = 10.7)
d. none of the above

Explanation:

Step1: Recall segment addition postulate

Given \( C \) is on \( \overline{AB} \), so \( AC + CB = AB \).

Step2: Substitute values of \( AC \) and \( CB \)

\( AC = 6.5 \), \( CB = 5.2 \), so \( AB = 6.5 + 5.2 \).

Step3: Calculate \( AB \)

\( 6.5 + 5.2 = 11.7 \)? Wait, no, wait: \( 6.5 + 5.2 = 11.7 \)? Wait, no, 6.5 + 5.2: 6 + 5 = 11, 0.5 + 0.2 = 0.7, so total 11.7? Wait, but option B is 11, option C is 10.7. Wait, maybe I misread. Wait, the diagram: A---6.5---C---5.2---B. So \( AC = 6.5 \), \( CB = 5.2 \). Then \( AB = AC + CB = 6.5 + 5.2 = 11.7 \)? But the options: A: \( AB = 2(AC) \)? \( 2(6.5)=13
eq 11.7 \). B: 11, no. C: 10.7, no. Wait, maybe I made a mistake. Wait, 6.5 + 5.2: 6.5 + 5 = 11.5, +0.2 = 11.7. So none of A (13), B (11), C (10.7) is correct? So the answer is D? Wait, but let's check again. Wait, maybe the numbers are 6.5 and 5.2. 6.5 + 5.2 = 11.7. So A: 2*6.5=13≠11.7. B:11≠11.7. C:10.7≠11.7. So the answer is D.

Wait, but maybe I misread the numbers. Let me check the diagram again. The user's image: A to C is 6.5, C to B is 5.2. So \( AB = AC + CB = 6.5 + 5.2 = 11.7 \). So option A: \( AB = 2(AC) \) would be 13, not 11.7. Option B: 11, no. Option C: 10.7, no. So the correct option is D.

Answer:

D. none of the above