Question 27 of 30 Use the midpoint formula to find the midpoint between \( S(3,5) \) and \( P(5,5) \). A. \( (0,1) \) B. \( (4.5,10) \) C. \( (4,5) \) D. \( (4.5,5) \)

To find the midpoint between the points \( S(3,5) \) and \( P(5,5) \), we apply the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Plugging in the coordinates of points \( S \) and \( P \): \[ M = \left( \frac{3 + 5}{2}, \frac{5 + 5}{2} \right) = \left( \frac{8}{2}, \frac{10}{2} \right) = (4, 5) \] So, the midpoint is \( (4,5) \), which corresponds to option C. Historical Background: The concept of the midpoint is rooted in basic geometry and can be traced back to ancient mathematicians who explored the idea of dividing lines evenly. This foundational idea has been integral to many fields, including construction, design, and even astronomy! Real-World Application: Midpoints are often used in mapping and navigation to find central locations or breaking up distances evenly between two points, like when you're coordinating a meeting spot or determining the equal distance between two landmarks. It helps ensure everyone travels the same amount, making it a key factor in planning outings or events!