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The coordinates of three vertices of parallelogram ABCDABCD are A(−1,0)A(-1,0), B(2,3)B(2,3), and C(3,2)C(3,2). What are coordinates of the fourth vertex and the point of intersection of the diagonals?

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Find the magnitude of a three-dimensional vectorright chevron icon

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Q. The coordinates of three vertices of parallelogram ABCDABCD are A(−1,0)A(-1,0), B(2,3)B(2,3), and C(3,2)C(3,2). What are coordinates of the fourth vertex and the point of intersection of the diagonals?
  1. Find AB AB and AC AC : Find vector AB AB and vector AC AC . AB=B−A=(2−(−1),3−0)=(3,3) AB = B - A = (2 - (-1), 3 - 0) = (3, 3) AC=C−A=(3−(−1),2−0)=(4,2) AC = C - A = (3 - (-1), 2 - 0) = (4, 2)
  2. Use vector addition: Use vector addition to find DD. D=A+(B−C)=(−1,0)+(2−3,3−2)=(−1,0)+(−1,1)=(−2,1)D = A + (B - C) = (-1, 0) + (2 - 3, 3 - 2) = (-1, 0) + (-1, 1) = (-2, 1)
  3. Find midpoints: Find midpoint of diagonals ACAC and BDBD. Midpoint of AC=(−1+32,0+22)=(1,1)AC = \left(\frac{-1 + 3}{2}, \frac{0 + 2}{2}\right) = (1, 1) Midpoint of BD=(2+(−2)2,3+12)=(0,2)BD = \left(\frac{2 + (-2)}{2}, \frac{3 + 1}{2}\right) = (0, 2)

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