6) Point \( M \) is the midpoint of \( A B \). If the coordinates of \( M \) are \( (2,8) \) and the coordinates of \( B \) are \( (10,12) \), what are the coordinates of \( A \) ? 7) \( M \) is the midpoint of \( A B \). If the coordinates of \( A \) are \( (-1,5) \) and the coordinates of \( B \) are \( (3,3) \), what are the coordinates of \( M \) ?

To find the coordinates of point \( A \) for the first question, you can use the midpoint formula, which is: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Here, \( M(2, 8) \) is the midpoint, and \( B(10, 12) \) is one endpoint. Let the coordinates of \( A \) be \( (x, y) \). Setting up the equations, we have: \[ 2 = \frac{x + 10}{2} \quad \text{and} \quad 8 = \frac{y + 12}{2} \] Solving these, we find \( x = -6 \) and \( y = 4 \). Thus, the coordinates of \( A \) are \( (-6, 4) \). For the second question, you can again use the midpoint formula. Given the coordinates of \( A(-1, 5) \) and \( B(3, 3) \): \[ M = \left( \frac{-1 + 3}{2}, \frac{5 + 3}{2} \right) \] Calculating that gives: \[ M = \left( \frac{2}{2}, \frac{8}{2} \right) = (1, 4) \] So, the coordinates of \( M \) are \( (1, 4) \).