(5) 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: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Now, let's calculate the midpoints for each pair: (i) For points \( (3,2) \) and \( (5,4) \): \[ \text{Midpoint} = \left( \frac{3 + 5}{2}, \frac{2 + 4}{2} \right) = \left( \frac{8}{2}, \frac{6}{2} \right) = (4, 3) \] (ii) For points \( (1,5) \) and \( (7,3) \): \[ \text{Midpoint} = \left( \frac{1 + 7}{2}, \frac{5 + 3}{2} \right) = \left( \frac{8}{2}, \frac{8}{2} \right) = (4, 4) \] (iii) For points \( (3,7) \) and \( (5,9) \): \[ \text{Midpoint} = \left( \frac{3 + 5}{2}, \frac{7 + 9}{2} \right) = \left( \frac{8}{2}, \frac{16}{2} \right) = (4, 8) \] (iv) For points \( (-1,4) \) and \( (5,6) \): \[ \text{Midpoint} = \left( \frac{-1 + 5}{2}, \frac{4 + 6}{2} \right) = \left( \frac{4}{2}, \frac{10}{2} \right) = (2, 5) \] The midpoints are: (i) \( (4, 3) \) (ii) \( (4, 4) \) (iii) \( (4, 8) \) (iv) \( (2, 5) \)