To find the midpoint of two points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] with given coordinates, we use the midpoint formula. The midpoint formula for points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given:
The coordinates of point [tex]\( A \)[/tex] are [tex]\((2, 3)\)[/tex], which means [tex]\( x_1 = 2 \)[/tex] and [tex]\( y_1 = 3 \)[/tex].
The coordinates of point [tex]\( B \)[/tex] are [tex]\((8, 9)\)[/tex], which means [tex]\( x_2 = 8 \)[/tex] and [tex]\( y_2 = 9 \)[/tex].
Step-by-step solution:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{2 + 8}{2} = \frac{10}{2} = 5
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{3 + 9}{2} = \frac{12}{2} = 6
\][/tex]
Therefore, the coordinates of the midpoint are [tex]\( (5, 6) \)[/tex].
So, the midpoint of points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is [tex]\( \boxed{(5, 6)} \)[/tex].
