The three vertices of a parallelogram taken in order are (0, 1), (−1, −2), and (2, 1). The coordinates of fourth vertex are ______.

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The three vertices of a parallelogram taken in order are (0, 1), (−1, −2), and (2, 1). The coordinates of fourth vertex are (3, 4). Explanation: In a parallelogram, the diagonals bisect each other, So the midpoint of AC: = ((0 + 2)/2, (1 + 1)/2) = (1, 1) Set this equal to the midpoint of BD: = ((-1+x)/2, (-2+y)/2) (Multiplying both sides by 2) = (−1 + x = 2), (−2 + y = 2) ∴ x = 3, y = 4

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