Answer:
B(6, 2) and D(2, -2)
Explanation:
Given points A(2, 2) and C(6, -2) on square ABCD, you want the coordinates of the other two vertices.
Aligned
We can check to see if the square is aligned with the coordinate grid by finding the slope of AC.
slope = (y2 -y1)/(x2 -x1) = (-2 -2)/(6 -2) = -4/4 = -1
The slope of -1 means the diagonal has a rise of -1 for each run of 1. The square is aligned with the grid, and each side is of length 4.
Vertices
We can choose point B to be 4 units to the right of A:
B = (2 +4, 2) = (6, 2)
And we can choose point D to be 4 units down from A:
D = (2, 2 -4) = (2, -2)
The remaining vertices are B(6, 2) and D(2, -2).
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Additional comment
We have chosen to name the vertices in clockwise order. If you prefer counterclockwise you can swap the labels B and D.
If the square were skew to the grid, we would use a different approach to finding the vertices. Basically, we could rotate the known vertices 90° around the center of the square using a rotation transformation.
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