Let's fill in the table step-by-step by calculating the distances and the orientation for each pair of coordinates:
1. Coordinates: [tex]\((-3, 9)\)[/tex] and [tex]\((-3, 1)\)[/tex]
\- Since both x-coordinates are the same, this is a vertical distance.
\- The distance between [tex]\(9\)[/tex] and [tex]\(1\)[/tex] is [tex]\(|9 - 1| = 8\)[/tex].
2. Coordinates: [tex]\((8, 2)\)[/tex] and [tex]\((-4, 2)\)[/tex]
\- Since both y-coordinates are the same, this is a horizontal distance.
\- The distance between [tex]\(8\)[/tex] and [tex]\(-4\)[/tex] is [tex]\(|8 - (-4)| = 12\)[/tex].
3. Coordinates: [tex]\((5, -4)\)[/tex] and [tex]\((5, 2)\)[/tex]
\- Since both x-coordinates are the same, this is a vertical distance.
\- The distance between [tex]\(-4\)[/tex] and [tex]\(2\)[/tex] is [tex]\(|-4 - 2| = 6\)[/tex].
4. Coordinates: [tex]\((3, 0)\)[/tex] and [tex]\((-6, 0)\)[/tex]
\- Since both y-coordinates are the same, this is a horizontal distance.
\- The distance between [tex]\(3\)[/tex] and [tex]\(-6\)[/tex] is [tex]\(|3 - (-6)| = 9\)[/tex].
5. Coordinates: [tex]\((2, -4)\)[/tex] and [tex]\((2, -1)\)[/tex]
\- Since both x-coordinates are the same, this is a vertical distance.
\- The distance between [tex]\(-4\)[/tex] and [tex]\(-1\)[/tex] is [tex]\(|-4 - (-1)| = 3\)[/tex].
6. Coordinates: [tex]\((0, -5)\)[/tex] and [tex]\((0, -1)\)[/tex]
\- Since both x-coordinates are the same, this is a vertical distance.
\- The distance between [tex]\(-5\)[/tex] and [tex]\(-1\)[/tex] is [tex]\(|-5 - (-1)| = 4\)[/tex].
7. Coordinates: [tex]\((1, 5)\)[/tex] and [tex]\((1, -4)\)[/tex]
\- Since both x-coordinates are the same, this is a vertical distance.
\- The distance between [tex]\(5\)[/tex] and [tex]\(-4\)[/tex] is [tex]\(|5 - (-4)| = 9\)[/tex].
Now, the completed table is:
\begin{tabular}{|c|c|c|}
\hline Coordinates & \begin{tabular}{c}
Distance between the \\
coordinates
\end{tabular} & \begin{tabular}{c}
Horizontal or \\
vertical
\end{tabular} \\
\hline[tex]$(-3,9)$[/tex] and [tex]$(-3,1)$[/tex] & 8 & Vertical \\
\hline[tex]$(8,2)$[/tex] and [tex]$(-4,2)$[/tex] & 12 & Horizontal \\
\hline[tex]$(5,-4)$[/tex] and [tex]$(5,2)$[/tex] & 6 & Vertical \\
\hline[tex]$(3,0)$[/tex] and [tex]$(-6,0)$[/tex] & 9 & Horizontal \\
\hline[tex]$(2,-4)$[/tex] and [tex]$(2,-1)$[/tex] & 3 & Vertical \\
\hline[tex]$(0,-5)$[/tex] and [tex]$(0,-1)$[/tex] & 4 & Vertical \\
\hline[tex]$(1,5)$[/tex] and [tex]$(1,-4)$[/tex] & 9 & Vertical \\
\hline
\end{tabular}
