To find the length of the segment [tex]\(\overline{GH}\)[/tex] given the coordinates of the points [tex]\(G(9,-1)\)[/tex] and [tex]\(H(9,6)\)[/tex], we approach it as follows:
1. Identify the coordinates of points [tex]\(G\)[/tex] and [tex]\(H\)[/tex]:
- Point [tex]\(G\)[/tex] has coordinates [tex]\((9, -1)\)[/tex].
- Point [tex]\(H\)[/tex] has coordinates [tex]\((9, 6)\)[/tex].
2. Notice that both points have the same x-coordinate:
- [tex]\( x_G = 9 \)[/tex] and [tex]\( x_H = 9 \)[/tex].
Since the x-coordinates are the same, [tex]\(\overline{GH}\)[/tex] is a vertical line.
3. Calculate the vertical distance:
- Vertical distance between two points with the same x-coordinate can be found by taking the absolute value of the difference between their y-coordinates.
- [tex]\( y_G = -1 \)[/tex] and [tex]\( y_H = 6 \)[/tex].
Therefore, the vertical distance [tex]\(GH\)[/tex] is given by:
[tex]\[
\left| y_H - y_G \right| = \left| 6 - (-1) \right| = \left| 6 + 1 \right| = \left| 7 \right| = 7
\][/tex]
Thus, the length of [tex]\(\overline{GH}\)[/tex] is [tex]\(7\)[/tex] units.
