1. **State the problem:** Find the lengths of the line segments \(\overline{CM}\) and \(\overline{AB}\) using the distance formula. 2. **Calculate \(CM\):** \[CM = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(1.5 - 0)^2 + (2 - 0)^2} = \sqrt{(1.5)^2 + 2^2} = \sqrt{2.25 + 4} = \sqrt{6.25} = 2.5\] 3. **Calculate \(AB\):** \[AB = \sqrt{(3 - 0)^2 + (0 - 4)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\] 4. **Compare the lengths:** - \(AB = 5\) - \(CM = 2.5\) 5. **Check the given options:** - a. \(AB = \frac{1}{2} CM\) is false because \(5 \neq \frac{1}{2} \times 2.5 = 1.25\) - b. \(CM = \frac{1}{2} AB\) is true because \(2.5 = \frac{1}{2} \times 5\) - c. 5 corresponds to \(AB\) - d. 2.5 corresponds to \(CM\) - e. 3.125 is not related **Final answers:** \[CM = 2.5, \quad AB = 5, \quad \text{and} \quad CM = \frac{1}{2} AB\]