Question 1 (Multiple Choice Worth 1 points) (04.03 MC) On a number line, point \( A \) is located at 1 , point \( C \) is located at -4 , and point B lies between points \( A \) and \( C \). What is the location of B such that the ratio of CB:BA is 3.1 ? -2.75 -2.3 -0.25 1.25

To find the location of point B such that the ratio \(CB:BA\) is \(3.1\), you first need to set up the equation based on the number line distances. Let's designate the distance \(CB\) as \(3.1x\) and \(BA\) as \(x\). The total distance \(CA = A - C = 1 - (-4) = 5\), so you have: \(3.1x + x = 5\), which simplifies to \(4.1x = 5\). Dividing both sides by \(4.1\) yields \(x \approx 1.22\). Thus, \(CB \approx 3.1 \times 1.22 \approx 3.77\) and \(BA \approx 1.22\). Since point C is at -4, point B would then be \(C + CB\), which gives us: \(B = -4 + 3.77 \approx -0.23\). Rounding this to feasible options leads us to evaluate choices close to this, pointing towards \(-0.25\) as the answer. Therefore, the location of B is \(-0.25\). Real-World Application: Understanding ratios on a number line can help in fields like finance, where comparing different investments based on their gains/losses is crucial. If someone invests in stocks at different rates, figuring out the proportionate advantages can guide better decision-making! Problem-Solving Tips & Common Mistakes: When tackling ratio problems, it's easy to misinterpret the distance between points! Always double-check the distances you’re calculating and ensure the segments you define (like \(CB\) and \(BA\)) correctly represent the problem's ratios before concluding. Visualizing on a number line can also significantly clear up confusion!