Question 5: The midpoint of \( (8, a) \) and \( (b, 14) \) is \( (11,10) \). The values of \( a \) and \( b \) are respectively
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To find the values of \( a \) and \( b \), we can use the midpoint formula. The midpoint \( (M_x, M_y) \) of two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ M_x = \frac{x_1 + x_2}{2}, \quad M_y = \frac{y_1 + y_2}{2} \] Given the points \( (8, a) \) and \( (b, 14) \), we know that the midpoint is \( (11, 10) \). Using the midpoint formula for the x-coordinates: \[ 11 = \frac{8 + b}{2} \] Multiplying both sides by 2 gives: \[ 22 = 8 + b \quad \Rightarrow \quad b = 22 - 8 = 14 \] Now for the y-coordinates: \[ 10 = \frac{a + 14}{2} \] Again, multiplying both sides by 2 gives: \[ 20 = a + 14 \quad \Rightarrow \quad a = 20 - 14 = 6 \] Thus, the values of \( a \) and \( b \) are 6 and 14, respectively.