rectangle has vertices at these coordinates. (0, 8), (5, 8), (5, 0) What are the coordinates of the fourth vertex of the rectangle?

Answer:   (0, 0)Step-by-step explanation:The given vertices lie on the horizontal line y=8 and the vertical line x=5. The vertices that do not lie on those lines have y=0 and x=0. These are the coordinates of the missing vertex: (x, y) = (0, 0)_____Alternate solutionThe diagonals of a rectangle have the same midpoint, so for rectangle ABCD, we have ...   midpoint(AC) = midpoint(BD)The midpoint of a line segment is the average of its endpoints, so this translates to ...   (A+C)/2 = (B+D)/2Multiplying by 2 and subtracting B gives ...   A + C = B + D   A + C - B = DSo, we can find the missing vertex by adding the coordinates of the diagonal and subtracting the third vertex:   (0, 8) + (5, 0) - (5, 8) = (0+5-5, 8+0-8) = (0, 0)The missing vertex is (0, 0).__Please note that this method works even if the rectangle's sides are not aligned with the axes.