Answer :
Let's fill in the table based on the given information.
### Given lines and their intersections:
1. The intersection point for lines [tex]\([(2, 5), (-3, -5)]\)[/tex] and [tex]\([(3, 0), (0, -3)]\)[/tex] is [tex]\((-4, -5)\)[/tex].
2. The intersection point for lines [tex]\([(1, 1), (2, 3)]\)[/tex] and [tex]\([(0, 3), (2, 5)]\)[/tex] is [tex]\((-3, -2)\)[/tex].
3. There are pairs of lines not used in the provided result and thus should not be added to the table.
4. The intersection point for lines [tex]\([(2, 0), (0, -2)]\)[/tex] and [tex]\([(4, 5), (3, 3)]\)[/tex] is [tex]\( (3, 4) \)[/tex].
Using this information, we can fill in the table as follows:
### Filled Table:
[tex]\[ \begin{tabular}{|c|c|c|} \hline Line 1 & Line 2 & Point of Intersection \\ \hline (2,5),(-3,-5) & (3,0),(0,-3) & (-4,-5) \\ \hline (1,1),(2,3) & (0,3),(2,5) & (-3,-2) \\ \hline (1,0),(0,-1) & (0,3),(-2,-1) & --- \\ \hline (2,0),(0,-2) & (4,5),(3,3) & (3,4) \\ \hline \end{tabular} \][/tex]
Therefore, the lines and their points of intersection are correctly matched.
### Given lines and their intersections:
1. The intersection point for lines [tex]\([(2, 5), (-3, -5)]\)[/tex] and [tex]\([(3, 0), (0, -3)]\)[/tex] is [tex]\((-4, -5)\)[/tex].
2. The intersection point for lines [tex]\([(1, 1), (2, 3)]\)[/tex] and [tex]\([(0, 3), (2, 5)]\)[/tex] is [tex]\((-3, -2)\)[/tex].
3. There are pairs of lines not used in the provided result and thus should not be added to the table.
4. The intersection point for lines [tex]\([(2, 0), (0, -2)]\)[/tex] and [tex]\([(4, 5), (3, 3)]\)[/tex] is [tex]\( (3, 4) \)[/tex].
Using this information, we can fill in the table as follows:
### Filled Table:
[tex]\[ \begin{tabular}{|c|c|c|} \hline Line 1 & Line 2 & Point of Intersection \\ \hline (2,5),(-3,-5) & (3,0),(0,-3) & (-4,-5) \\ \hline (1,1),(2,3) & (0,3),(2,5) & (-3,-2) \\ \hline (1,0),(0,-1) & (0,3),(-2,-1) & --- \\ \hline (2,0),(0,-2) & (4,5),(3,3) & (3,4) \\ \hline \end{tabular} \][/tex]
Therefore, the lines and their points of intersection are correctly matched.