8) Find the midpoints of the line segments joining the following pairs of points: \( \begin{array}{ll}\text { (i) }(3,2) \text { and }(5,4) & \text { (ii) }(1,5) \text { and }(7,3) \\ \text { (iii) }(3,7) \text { and }(5,9) & \text { (iv) }(-1,4) \text { and }(5,6)\end{array} \)

To find the midpoints of the line segments joining the given pairs of points, we use the midpoint formula: \[ M(x, y) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Applying this to each pair: (i) For points (3,2) and (5,4): \[ M = \left( \frac{3 + 5}{2}, \frac{2 + 4}{2} \right) = \left( \frac{8}{2}, \frac{6}{2} \right) = (4, 3) \] (ii) For points (1,5) and (7,3): \[ M = \left( \frac{1 + 7}{2}, \frac{5 + 3}{2} \right) = \left( \frac{8}{2}, \frac{8}{2} \right) = (4, 4) \] (iii) For points (3,7) and (5,9): \[ M = \left( \frac{3 + 5}{2}, \frac{7 + 9}{2} \right) = \left( \frac{8}{2}, \frac{16}{2} \right) = (4, 8) \] (iv) For points (-1,4) and (5,6): \[ M = \left( \frac{-1 + 5}{2}, \frac{4 + 6}{2} \right) = \left( \frac{4}{2}, \frac{10}{2} \right) = (2, 5) \] In summary, the midpoints are: (i) (4, 3) (ii) (4, 4) (iii) (4, 8) (iv) (2, 5)