Answer :

To find the midpoint of the points [tex]\((5, 7)\)[/tex] and [tex]\((3, 9)\)[/tex], we use the midpoint formula. The midpoint [tex]\(M\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Here are the coordinates of the given points:
[tex]\[ (x_1, y_1) = (5, 7) \quad \text{and} \quad (x_2, y_2) = (3, 9) \][/tex]

Substitute the coordinates into the midpoint formula:

1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{5 + 3}{2} = \frac{8}{2} = 4.0 \][/tex]

2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{7 + 9}{2} = \frac{16}{2} = 8.0 \][/tex]

Therefore, the midpoint of the points [tex]\((5, 7)\)[/tex] and [tex]\((3, 9)\)[/tex] is:

[tex]\[ (4.0, 8.0) \][/tex]