Question

on a number line, point a is located at 4, point c is located at 11, and point b lies between points a and c. what is the location of b such that the ratio of ab bc is 2:3? 8.2 6.8 5.9 5.6

Explanation:

Step1: Let the location of \( B \) be \( x \).

The distance \( AB=x - 4 \) (since \( A = 4 \) and \( B=x \)), and the distance \( BC = 11 - x \) (since \( C = 11 \) and \( B=x \)).

Step2: Use the ratio formula.

Given \( \frac{AB}{BC}=\frac{2}{3} \), substitute \( AB=x - 4 \) and \( BC = 11 - x \) into the ratio: \( \frac{x - 4}{11 - x}=\frac{2}{3} \).

Step3: Cross - multiply.

Cross - multiplying gives \( 3(x - 4)=2(11 - x) \).
Expand both sides: \( 3x-12 = 22-2x \).

Step4: Solve for \( x \).

Add \( 2x \) to both sides: \( 3x + 2x-12=22-2x + 2x \), so \( 5x-12 = 22 \).
Add \( 12 \) to both sides: \( 5x-12 + 12=22 + 12 \), then \( 5x=34 \).
Divide both sides by \( 5 \): \( x=\frac{34}{5}=6.8 \).

Answer:

\( 6.8 \)