The midpoint of \( (3, a) \) and \( (b, 10) \) is \( (6,7) \). The values of \( a \) and \( b \) are respectively

To find the values of \( a \) and \( b \), we can use the midpoint formula. The midpoint \( M \) of two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Here, the midpoint is \( (6, 7) \) and corresponds to the points \( (3, a) \) and \( (b, 10) \). This means: 1. For the x-coordinates: \[ \frac{3 + b}{2} = 6 \] Multiplying both sides by 2: \[ 3 + b = 12 \] Subtracting 3 from both sides: \[ b = 9 \] 2. For the y-coordinates: \[ \frac{a + 10}{2} = 7 \] Multiplying both sides by 2: \[ a + 10 = 14 \] Subtracting 10 from both sides: \[ a = 4 \] Thus, the values of \( a \) and \( b \) are respectively: \[ \boxed{4} \text{ and } \boxed{9} \]