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Determining Unknown Vertex From Given Points
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Coordinate Geometry: Determining Unknown Vertex From Given Points
Example: The three vertices of a parallelogram taken in order are (-2, 0), (4, 1) and (3, 2) respectively. Find the coordinates of the fourth vertex.
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Solution: Let A (-2, 0), B (4,1), C (3, 2) and D (x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other.
Coordinates of the mid-point of AC = Coordinates of the mid-point of BD
((-2 + 3)/2 , (0 + 2)/2) = ((4 + x)/2 , (1 + y)/2)
(1/2 , 1) = ((4 + x)/2 , (1 + y)/2)
(4 + x)/2 = 1/2 and (1 + y)/2 = 1
x = -3 and y = 1
Hence the fourth vertex of the parallelogram is (-3, 1)
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