Question Find the midpoint of the segment with the following endpoints. \[ (1,1) \text { and }(-7,7) \]

To find the midpoint of the segment with endpoints \( (1,1) \) and \( (-7,7) \), you can use the midpoint formula, which is given by: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the coordinates into the formula: \[ \left( \frac{1 + (-7)}{2}, \frac{1 + 7}{2} \right) = \left( \frac{-6}{2}, \frac{8}{2} \right) = (-3, 4) \] So, the midpoint of the segment is \( (-3, 4) \). Finding midpoints isn’t just useful in geometry; it's also a handy method in various fields like computer graphics and game design. For instance, when creating smooth transition animations between two points, the midpoint helps determine where to position intermediate graphics, making everything appear cohesive and visually appealing without any stumbling blocks. Moreover, think of this in real-life situations! If you're coordinating a meetup between friends at two different locations, using the midpoint allows you to find a perfect spot that balances travel for everyone. Next time you grab coffee or plan a picnic, use this simple formula to ensure optimal convenience for all involved!