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If A(-2,-1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, then find the values of a and b.
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Sol. Coordinates of the mid-point of AC = Coordinates of the mid-point of BD
$(\frac{-2+4}{2}, \frac{-1+b}{2}) = (\frac{a+1}{2}, \frac{0+2}{2})$
$\therefore \frac{-2+4}{2} = \frac{a+1}{2} \Rightarrow a=1$ (1/2 Mark)
and $\frac{-1+b}{2} = \frac{0+2}{2} \Rightarrow b=3$ (1/2 Mark)
$(\frac{-2+4}{2}, \frac{-1+b}{2}) = (\frac{a+1}{2}, \frac{0+2}{2})$
$\therefore \frac{-2+4}{2} = \frac{a+1}{2} \Rightarrow a=1$ (1/2 Mark)
and $\frac{-1+b}{2} = \frac{0+2}{2} \Rightarrow b=3$ (1/2 Mark)