To find the midpoint of two points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] with given coordinates, we can use the midpoint formula. The midpoint formula is:
[tex]\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the coordinates of point [tex]\( A \)[/tex] are [tex]\( (8, 5) \)[/tex], which means [tex]\( x_1 = 8 \)[/tex] and [tex]\( y_1 = 5 \)[/tex]. The coordinates of point [tex]\( B \)[/tex] are [tex]\( (3, 7) \)[/tex], which means [tex]\( x_2 = 3 \)[/tex] and [tex]\( y_2 = 7 \)[/tex].
Substitute these values into the midpoint formula:
[tex]\[
\text{Midpoint} = \left( \frac{8 + 3}{2}, \frac{5 + 7}{2} \right)
\][/tex]
First, calculate the [tex]\( x \)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{8 + 3}{2} = \frac{11}{2} = 5.5
\][/tex]
Next, calculate the [tex]\( y \)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{5 + 7}{2} = \frac{12}{2} = 6.0
\][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[
\left( 5.5, 6.0 \right)
\][/tex]
So, the midpoint of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is [tex]\((5.5, 6.0)\)[/tex].
