Answer:
To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.
Method 1: The fourth vertex is directly below the first vertex.
In this case, the coordinates of the fourth vertex are (5, 9), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
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Method 2: The fourth vertex is directly to the right of the first vertex.
In this case, the coordinates of the fourth vertex are (1, 5), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
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X . . . . . . . . .
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Method 3: The fourth vertex is diagonal to the first vertex.
In this case, the coordinates of the fourth vertex are (5, 5), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
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. . . X . . . . .
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Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).