The midpoint of \( (2, a) \) and \( (b, 7) \) is \( (4,5) \). 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: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] For the points \( (2, a) \) and \( (b, 7) \), the midpoint is given as \( (4, 5) \). From the x-coordinates, we have: \[ \frac{2 + b}{2} = 4 \] Multiplying both sides by 2 gives: \[ 2 + b = 8 \implies b = 6 \] From the y-coordinates, we have: \[ \frac{a + 7}{2} = 5 \] Multiplying both sides by 2 gives: \[ a + 7 = 10 \implies a = 3 \] Thus, the values of \( a \) and \( b \) are respectively \( 3 \) and \( 6 \). Answer: \( a = 3 \), \( b = 6 \)