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The three vertices of a parallelogram ABCD are A(3,−4), B(−1,−3) and C(−6,2). Find the coordinates of vertex D.

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(2, 1)

(- 2, 1)

(-2, -1)

(2, - 1)

answer is B.

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Detailed Solution

Let D be (a, b) and O be the midpoint of parallelogram

O is midpoint of AC = (\frac{3 - 6}{2}, \frac{- 4 + 2}{2})

= (- \frac{3}{2}, - 1)

O is also midpoint of BD = (\frac{- 1 + a}{2}, \frac{- 3 + b}{2})

\Rightarrow (- \frac{3}{2}, - 1) = (\frac{- 1 + a}{2}, \frac{- 3 + b}{2})

- \frac{3}{2} = (\frac{- 1 + a}{2}) and - 1 = (\frac{- 3 + b}{2})

a = - 2 and b = 1

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