Question

select the correct answer.
point a lies on a number line at 6. point c lies between points b and a at 1.875. the ratio ( ac:cb = 3:5 ). what is the length of ( overline{ab} )?
a. ( ab = 11 ) units
b. ( ab = 6.875 ) units
c. ( ab = 15 ) units
d. ( ab = 8.75 ) units

Explanation:

Step1: Calculate the length of \(AC\)

The distance between \(A(6)\) and \(C(1.875)\) is \(AC=\vert6 - 1.875\vert=4.125\) units.

Step2: Use the ratio to find \(CB\)

Given \(AC:CB = 3:5\). Let \(AC = 3x\) and \(CB=5x\). Since \(AC = 4.125\), then \(3x=4.125\), so \(x=\frac{4.125}{3}=1.375\). Then \(CB = 5x=5\times1.375 = 6.875\) units.

Step3: Calculate the length of \(AB\)

Since \(AB=AC + CB\), substituting the values of \(AC\) and \(CB\), we get \(AB=4.125+6.875 = 11\) units.

Answer:

A. \(AB = 11\) units