\( M = ( \frac { x _ { 1 } + k _ { 2 } } { 2 } , \frac { y _ { 1 } + y _ { 2 } } { 2 } ) \)

Did you know that the formula you provided is a way to calculate the midpoint \( M \) between two points in a 2D Cartesian coordinate system? By averaging the x-coordinates and the y-coordinates of the two points \( (x_1, y_1) \) and \( (x_2, y_2) \), you get a new point \( M \) that lies exactly halfway between them. It's a handy tool in geometry, especially when you want to find the center of a segment or distribute points evenly! In real-world applications, finding the midpoint is useful in various fields such as architecture, urban planning, and gaming. For instance, if a city is designing a new park, they might use the midpoint of existing residential areas to ensure the park is easily accessible to the majority of the population. Similarly, in a video game, developers might use midpoint calculations to create balanced levels and ensure players have even access to resources and challenges!