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

To find the values of \( a \) and \( b \), we can use the midpoint formula, which states that the midpoint \( M \) of a segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given the points \( (a, 3) \) and \( (10, b) \), their midpoint is \( (7, 6) \). Using the coordinates for the midpoint: 1. For the x-coordinates: \[ \frac{a + 10}{2} = 7 \] Multiply both sides by 2: \[ a + 10 = 14 \] Solve for \( a \): \[ a = 14 - 10 = 4 \] 2. For the y-coordinates: \[ \frac{3 + b}{2} = 6 \] Multiply both sides by 2: \[ 3 + b = 12 \] Solve for \( b \): \[ b = 12 - 3 = 9 \] Thus, the values of \( a \) and \( b \) are \( 4 \) and \( 9 \), respectively. The final answer is \( a = 4 \) and \( b = 9 \).