Use the midpoint formula to find the midpoint between \( H(3,12) \) and \( J(9,-2) \). \[ \begin{array}{l}\text { A. }(6,5) \\ \text { B. }(4,5.5) \\ \text { C. }(14,11) \\ \text { D. }(7,3.5)\end{array} \]

To find the midpoint between points \( H(3,12) \) and \( J(9,-2) \), we apply the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting in our values: \[ M = \left( \frac{3 + 9}{2}, \frac{12 + (-2)}{2} \right) = \left( \frac{12}{2}, \frac{10}{2} \right) = (6, 5) \] So the midpoint is \( (6, 5) \). The correct answer is **A. (6, 5)**. Finding the midpoint is like having a friendly debate about two points - you just average out their positions! Just imagine H and J sitting down in the middle, meeting halfway. That's exactly what the midpoint finds! Additionally, it's important to remember that when applying the formula, you should carefully add the x-coordinates and the y-coordinates separately. A common mistake is to mix up the signs or arithmetic when adding the negative y-coordinate, leading to incorrect results. Always double-check your calculations!