Final answer:
The midpoint of the line segment with endpoints (-(6)/(5),-(1)/(6)) and ((7)/(5),(7)/(6)) is (\( \frac{1}{2} \), \( \frac{3}{4} \)). This is found by averaging the x-coordinates and the y-coordinates separately.
Step-by-step explanation:
Finding the Midpoint of a Line Segment
To find the midpoint of a line segment with endpoints (-(6)/(5),-(1)/(6)) and ((7)/(5),(7)/(6)), you can use the midpoint formula. This formula involves taking the average of the x-coordinates and the average of the y-coordinates separately to find the midpoint. The midpoint M can be calculated as:
M = \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
For our points, we have:
M = \( \left( \frac{-\frac{6}{5} + \frac{7}{5}}{2}, \frac{-\frac{1}{6} + \frac{7}{6}}{2} \right) \) = \( \left( \frac{1}{2}, \frac{3}{4} \right) \)
So the midpoint of the line segment is (\( \frac{1}{2} \), \( \frac{3}{4} \)).