To find the midpoint of a line segment with endpoints [tex]\( A(x_1, y_1) \)[/tex] and [tex]\( B(x_2, y_2) \)[/tex], you can use the midpoint formula. The midpoint formula is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given points [tex]\( A(8,2) \)[/tex] and [tex]\( B(6,4) \)[/tex]:
1. Identify the coordinates of point [tex]\( A \)[/tex]:
[tex]\[
A(8, 2)
\][/tex]
2. Identify the coordinates of point [tex]\( B \)[/tex]:
[tex]\[
B(6, 4)
\][/tex]
3. Apply the midpoint formula:
- Calculate the x-coordinate of the midpoint:
[tex]\[
M_x = \frac{8 + 6}{2} = \frac{14}{2} = 7.0
\][/tex]
- Calculate the y-coordinate of the midpoint:
[tex]\[
M_y = \frac{2 + 4}{2} = \frac{6}{2} = 3.0
\][/tex]
4. Combine the x and y coordinates to form the midpoint as an ordered pair:
[tex]\[
M = (7.0, 3.0)
\][/tex]
Therefore, the midpoint of the line segment with endpoints [tex]\( A(8,2) \)[/tex] and [tex]\( B(6,4) \)[/tex] is [tex]\((7.0, 3.0)\)[/tex].
