Three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2). The coordinates of the fourth vertex are:
Answer: A
In a parallelogram, the diagonals bisect each other. This means the midpoint of one diagonal is the same as the midpoint of the other diagonal.
Let the vertices be A(-1, 0), B(3, 1), C(2, 2), and D(x, y).
Midpoint of diagonal AC = \((\frac{-1+2}{2}, \frac{0+2}{2}) = (1/2, 1)\).
Midpoint of diagonal BD = \((\frac{3+x}{2}, \frac{1+y}{2})\).
Equating the midpoints: \(\frac{3+x}{2} = \frac{1}{2} \Rightarrow 3+x=1 \Rightarrow x=-2\).
\(\frac{1+y}{2} = 1 \Rightarrow 1+y=2 \Rightarrow y=1\).
The fourth vertex is (-2, 1).