Find the midpoint of the segment having endpoints \( \left(0, \frac{1}{4}\right) \) and \( \left(-\frac{4}{5}, 0\right) \)

To find the midpoint of a segment with endpoints \( \left(0, \frac{1}{4}\right) \) and \( \left(-\frac{4}{5}, 0\right) \), we use the midpoint formula, which states that the midpoint \( M(x, y) \) can be calculated using: \[ M\left(x, y\right) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \] Here, the coordinates are: - \( x_1 = 0 \), \( y_1 = \frac{1}{4} \) - \( x_2 = -\frac{4}{5} \), \( y_2 = 0 \) Now, we will compute each coordinate of the midpoint: **For the x-coordinate:** \[ \frac{x_1 + x_2}{2} = \frac{0 + \left(-\frac{4}{5}\right)}{2} = \frac{-\frac{4}{5}}{2} = -\frac{4}{10} = -\frac{2}{5} \] **For the y-coordinate:** \[ \frac{y_1 + y_2}{2} = \frac{\frac{1}{4} + 0}{2} = \frac{\frac{1}{4}}{2} = \frac{1}{8} \] Putting it all together, the midpoint \( M \) of the segment is: \[ M\left(-\frac{2}{5}, \frac{1}{8}\right) \] So, the final answer is: \[ \boxed{\left(-\frac{2}{5}, \frac{1}{8}\right)} \]