Consider A(3, 4), B (3, 8) and C(9, 8).
Let the coordinates of fourth vertex are D (x, y)
In a parallelogram diagonals bisect each other
Coordinate of mid point of AC = X = \(\frac{3 + 9}2\) = \(\frac{12}2\) = 6
Y = \(\frac{4 + 8}2\) = \(\frac{12}2\) = 6
Therefore coordinates of mid point of AC are (6, 6) Coordinate of mid point of BD = X = \(\frac{3 + x}2\)
Y = \(\frac{y + 8}2\)
Coordinates of point D are
\(\frac{3 + x}2\) = 6
x = 12 - 3 = 9
\(\frac{y + 8}2\) = 6
y = 12 - 8 = 4
Therefore coordinates of fourth vertex D are (9, 4)
