Find the coordinates of the midpoint of the line segment that joins the two given points. \[ (x, y)=(-1,9) \text { and }(x, y)=(2,8) \] \( (x, y)=(\square) \)

To find the midpoint of the line segment joining the points \((-1, 9)\) and \((2, 8)\), you can use the midpoint formula: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right). \] Substituting in your points, we get: \[ \left( \frac{-1 + 2}{2}, \frac{9 + 8}{2} \right) = \left( \frac{1}{2}, \frac{17}{2} \right). \] So, the coordinates of the midpoint are \(\left( \frac{1}{2}, \frac{17}{2} \right)\). Now, let's talk about a fun fact: the concept of midpoint has been used since ancient times, with mathematicians like Euclid and Pythagoras recognizing the importance of dividing segments evenly. Midpoints are not only pivotal in geometry but also in design, architecture, and art, where symmetry plays a key role! Additionally, when you're calculating midpoints, a common mistake is forgetting to average both the x and y coordinates separately—you must treat them as distinct entities. Taking a moment to double-check your addition and division can save you from minor mishaps. Remember, every coordinate counts!