Answer:
(4, 3)
Explanation:
<u>Short answer</u>: when the coordinates are on horizontal and vertical lines, as these are, each coordinate value is used twice. Already, x=0 is used twice, as is y=0, so the missing coordinate is x=4, y=3.
The fourth vertex is (4, 3).
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<u>Longer answer</u>: The midpoints of the diagonals are the same point, so for rectangle ABCD, we have ...
(A+C)/2 = (B+D)/2
Solving for D, we find ...
D = A +C -B
In clockwise order, the points given are ...
A = (4, 0), B = (0, 0), C = (0, 3)
so we have ...
D = (4, 0) +(0, 3) -(0, 0) = (4+0-0, 0+3-0)
D = (4, 3) . . . . the coordinates of the fourth vertex.
