Answer:
The mid point of the line segment is [tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex].
Step-by-step explanation:
From the graph we can find the end points of the line segment. The end points are: [tex]$ (- 1, - 4) $[/tex] and [tex]$ (4, 1) $[/tex].
When the end points of a line segment are known, the mid point of the line segment is given by:
[tex]$ \bigg ( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg ) $[/tex]
where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the end points.
Here: [tex]$ (x_1, y_1) = (- 1, - 4) $[/tex] and [tex]$ (x_2, y_2) = (4, 1) $[/tex]
Therefore, the mid point of the line segment would be:
[tex]$ \bigg ( \frac{- 1 + 4}{2}, \frac{- 4 + 1}{2} \bigg) $[/tex]
[tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex] is the required answer.
