5. Find the coordinates for the midpoint of \( M N \) with endpoints \( M(11,-4) \) and \( N(-7,6) \) ? The Midpoint Formiula \( \left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) \)

To find the midpoint \( P \) of the line segment \( MN \), use the midpoint formula. Here, \( M(11, -4) \) and \( N(-7, 6) \) give us coordinates \( x_1 = 11 \), \( y_1 = -4 \), \( x_2 = -7 \), and \( y_2 = 6 \). Plugging these values into the formula, we have: \[ P = \left(\frac{11 + (-7)}{2}, \frac{-4 + 6}{2}\right) = \left(\frac{4}{2}, \frac{2}{2}\right) = (2, 1) \] So, the midpoint is \( P(2, 1) \). While the midpoint formula is super handy, many people forget to check whether they’re averaging the correct coordinates. A classic mistake is to mix up the \( x \) and \( y \) values, leading to a wildly incorrect midpoint. Always double-check your values and calculations to avoid this pitfall!