Answer:
[tex](5,\, -2)[/tex].
Step-by-step explanation:
For a line segment in a plane, the [tex]x[/tex]-coordinates of the midpoint is the average of the [tex]x\![/tex]-coordinates of the endpoints. Likewise, the [tex]y[/tex]-coordinates of the midpoint is the average of the [tex]y\![/tex] coordinates of the endpoints.
For example, the midpoint of the line segment joining [tex](x_{a},\, y_{a})[/tex] and [tex](x_{b},\, y_{b})[/tex] is:
[tex]\begin{aligned} \left(\frac{x_{a} + x_{b}}{2},\, \frac{y_{a} + y_{b}}{2}\right)\end{aligned}[/tex].
In this question, [tex]x_{a} = 8[/tex], [tex]x_{b} = 2[/tex], [tex]y_{a} = (-5)[/tex], [tex]y_{b} = 1[/tex]. Thus, the midpoint of the line segment joining the two points would be:
[tex]\begin{aligned} \left(\frac{8 + 2}{2},\, \frac{(-5) + 1}{2}\right)\end{aligned}[/tex].
Simplify to obtain:
[tex]\begin{aligned} \left(5,\, -2\right)\end{aligned}[/tex].
Hence, the midpoint of the line segment joining [tex](8,\, -5)[/tex] and [tex](2,\, 1)[/tex] would be [tex](5,\, -2)[/tex].