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If the points A$(4, 5)$, B$(m, 6)$, C$(4, 3)$ and D$(1, n)$ taken in this order are the vertices of a parallelogram ABCD, then find the values of $m$ and $n$.
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Sol. Coordinates of mid-point of AC = Coordinates of mid-point of BD (1 Mark)
$\frac{4+4}{2}$, $\frac{5+3}{2}$) = ($\frac{1+m}{2}$, $\frac{n+6}{2}$) (1 Mark)
m = 7 (1/2 Mark)
n = 2 (1/2 Mark)
$\frac{4+4}{2}$, $\frac{5+3}{2}$) = ($\frac{1+m}{2}$, $\frac{n+6}{2}$) (1 Mark)
m = 7 (1/2 Mark)
n = 2 (1/2 Mark)